The answer to this question really depends on how you draw the lines between religions. Depending on how you want to do the dividing, there are between one and several thousand Abrahamic religions.

As a case study, let's talk about Christianity (it's what I know best). When you talk about Christianity, which Christianity do you mean? Looking at the first five hundred years of Christianity, should we talk about Nicene and Arian Christians as the same religion? What about Montanist and gnostic Christians? Is Christianity within the Roman Empire the same religion as the Christianity practiced outside it? The earliest Christians were adamant that to be a soldier was a sin, as it violated the prohibition against murder. Would they have recognized the crusaders as practicing the same religion? Fast forward to the Great Schism between East and West in 1053 CE. Roman Catholicism and Eastern Orthodoxy have now been officially separated for almost as long as Christianity has been a thing, even if you start counting at Jesus's birth. At what point do we start talking about them as different religions? Can they officially start seeing other people, or is this one of those "once a couple, always a couple" things? If that's the case, why isn't Christianity still technically Judaism? It could be, but more on that in a bit!

Because hold on. Is Christianity even a religion? For a while, the Romans weren't so sure. Robert Louis Wilken documents this question well in his The Christians as the Romans Saw Them. Some Romans thought Christianity was a burial society, a kind of social eating club mixed with funeral insurance (you pay annual dues, the society covers your funeral expenses). Some thought it was a political organization, kind of like a grassroots faction. Some thought it was more a philosophy, and indeed, early Christian thinkers preferred the label "philosopher" to "theologian," which had pagan undertones. Some considered them atheists because they refused to participate in the imperial cult. A lot of this came down to bad or faulty information—Romans accused Christians of being cannibals ("They have a meal where they eat someone's body and blood!") and incestuous ("Husband and wife refer to one another as 'brother' and 'sister!'"). But the point stands that it's sometimes only retroactively that we see something as being a religion, and that definition is culturally dependent. Is a secular nation state a kind of religion? It might be harder to say no than you might think. Looking around us today, you and I might not think of football or CrossFit as religions, but an alien visiting our planet might. Give it two or three hundred years, and you might too!

OK, for the sake of argument, let's concede that Christianity is a religion. When does it start? Jesus of Nazareth and his disciples were all Jewish, they worshipped in synagogues, they observed the Passover, they visited the temple in Jerusalem. Jesus was referred to as a Rabbi and came not to abolish the law but to fulfill it (allegedly). Some supposed he was the prophet Elijah come again, or so it was said. Wouldn't his followers also be Jews? If not, when do the followers of Jesus of Nazareth stop being a movement within Judaism and start being their own religion? It's hard to say, and there is no consensus among historians about when or how to differentiate the two. A main theme of the letters of Paul of Tarsus is his perspective on the lively debate over how followers of Jesus ought to obey the law of Moses or not. Some Christians insisted that it must be obeyed in full by gentile (that is, non-Jewish) followers of Jesus. Others went so far as to claim that the God of the Jews was a different, lesser God than the one Jesus addressed as "Father." Accordingly, these Christians (called "Marcionites") rejected the Hebrew Bible as Scripture and instead created their own canon of texts. The New Testament that you and I know today has its origins as a counter-canon to the Marcionite canon. This conflict has led some scholars, like Daniel Boyarin in Dying for God: Martyrdom and the Making of Christianity and Judaism, to make the case that until at least the Council of Nicaea in 325 CE, what we have is one religion on a spectrum between Rabbinical Judaism on the one end and Marcionism on the other, with Nicene Christianity somewhere in the middle. It seems insane to us today to imagine Christianity not being, well, Christianity for several hundred years after Jesus of Nazareth's life and death, but that's just the way some things might shake out! We shouldn't sweat it though. Whenever we start to call it Christianity has much more to do with us and how we are thinking about the past and much less to do with what actually happened. Or to put it differently, labels are our way of understanding the past and making meaning from it. They have precious little to do with the way things were, one way or another.

So you see, the question of how to count religions is particularly thorny and reveals more about us than about the past or reality (whatever that is). This isn't to say that the category of "Abrahamic" religions isn't helpful, though! It helps us talk about the history of different movements, their origins and interconnectedness, how they understood one another, etc. But religions as a thing we can number and count, well, that's where even the category of 'religion' starts to break down. We see it first in categories like "Christianity" or "Abrahamic," which is why this question is so instructive. Asking it helps us examine our own ideas and preconceptions, which is the first step in good historical inquiry into something as expansive as religion. So good on you for asking the question, and keep going where it takes you!

There are other Abrahamic religions that have formed historically as sects from these three, or as relatively new religious movements that are partly inspired by them (Baha’i), and others that may or may not be recognised as part of these religions depending on whom you ask (the Mormons and Jehovah’s Witnesses certainly self-identify as Christian, while many major ‘traditional’ churches do not see them as such).

So as not to get into the very controversial cases of religions founded in modern times, let’s restrict this to those that were founded in ancient and medieval times, but still exist. I’ll try to give an overview of three major examples and why they fit the criteria, which I’ll use as ‘having historically largely developed from an established Abrahamic religion’, and possibly ‘according the figure of Abraham special status as a prophet or similar authority or precursor.’

Samaritanism is probably the most ancient ‘fourth’ Abrahamic religion, older than Christianity and Islam, and can be seen as ‘alternate timeline’ Judaism, or Judaism’s sister religion. They’re most well known through the parable of the Good Samaritan, but there are about a thousand still left in both Israel and the West Bank. They have their own version of the Torah, with subtle differences and in a slightly different ‘Samaritan’ Hebrew. From Jesus’ time they were seen by many Jews as ‘fake Hebrews’ who were really Gentiles from the Assyrian Empire, and their centre of worship was Mount Gerizim rather than the Temple in Jerusalem, a fact the Jews generally saw as unacceptable. It seems they are the one group with a real claim to continuity with any of the Northern Kingdom (which fell to the Assyrians before the southern ‘Jewish’ kingdom of Judah fell to Babylon), or the ‘Lost Ten Tribes’ of Israel (by tradition, the tribe of Ephraim, son of Joseph), appearing to descend largely from Israelite men and women from elsewhere in the Middle East, possibly brought in by the Assyrians, so in a sense it appears both narratives had a grain of truth. The post-diasporic Jewish convention of recognising the female line adds some new ‘legitimacy’ that was lacking in Jesus’ patrilineal time. They are thus essentially the small exception of Hebrews today who are not Jews. They are certainly Abrahamic.

The Mandaeans of southern Iraq (many of the remaining few tens of thousands scattered by the recent wars) are essentially, according to a numbers of scholars, the last true remaining branch of ancient Gnosticism, from the first few centuries AD. The consensus has shifted over the last century (especially since the discovery of the Nag Hammadi library) from seeing the Gnostics as pre-Christian philosophical schools that incorporated Christian elements as it became socially and politically wise to do so, to early Christian-based sects that incorporated pre-Christian elements. The origins and even original beliefs of the Mandaeans in particular are obscure, and are still varied, but from the early Islamic era we have records of them proclaiming their reverence for John the Baptist, and some see Jesus as a ‘usurper’ of John’s role of major prophet. Baptism is a major part of their ritual life, and their beliefs include aspects of cosmology, the nature of God, and eschatology that are similar to other Gnostic traditions. There is a lot of debate among secular scholars about the degree to which they can be claimed to have basis in Christianity (internally, Mandaeans would not like this idea), but there are undeniably ultimately key Jewish elements in the religion. They do not, however, recognise the prophethood of Abraham or Moses either (though they recognise both John the Baptist and others who are key in Judaism), so calling them ‘Abrahamic’ might be a thorny semantic issue. It is reasonable from the available evidence, and what we can now deduce about the history of Gnosticism, that they are based on Abrahamic religion.

The Druze are another, far more numerous group, numbering over a million. They may or may not fit the criteria I specified above, since not everyone agrees on their status as a separate religion and they were founded much later (around 1000 AD), in Egypt, at the time of the Ismaili Shia Fatimids, and accounts differ very strongly: the Fatimid Caliph al-Hakim was particularly repressive of non-Muslims and Muslims outside his Ismaili Shi’i sect, and the most commonly recognised founder of the Druze, Hamza ibn-Ali ibn-Ahmad, for reasons complex and unknown, but possibly in a misguided attempt to placate the Caliph, declared al-Hakim to be divine. This resulted in his execution. Other versions are that he claimed no such thing, and the significance of the exact sequence of events, as well as exactly what Hamza ibn-Ali ibn-Ahmad believed, are sensitive and highly disputed. Regardless, the Druze community eventually shifted to Mount Lebanon, eventually coming to rule much of the area. They also incorporate mystical elements sometimes seen as Gnostic or Sufi in basis, as well as such unusual beliefs among the Abrahamic religions as reincarnation. Most Muslims do not recognise them as Muslims, and about half of Druze (from memory; will check the source of this stat) consider Druze to be a separate religion from Islam, though with a great deal of intersection. There are of course many other esoteric sects with a pedigree that are regarded with varying levels of suspicion by most members of the major religion, but Druze has a more widely recognised separate status, and this is recognised politically in Lebanon. Much of the religion is still clearly grounded in Islam, and it developed within an Islamic context, its earliest adherents being Muslims, and they do see Abraham as a significant figure in a similar way - so ‘Abrahamic’ applies.

Well, the word "Abrahamic" isn't as clear as you may think. Religious Studies professor Aaron Hughes wrote a book on the problems with the phrase Abrahamic religions, arguing:

“Abrahamic religions” are [often] assumed to consist of a set of essential characteristics that can be juxtaposed with other religions, be they “Eastern,” “pagan,” “new,” or “mixed”...[The usages of this term] are used to illumine some deep, essential, or necessary trait that somehow makes them unique from all other (“non-Abrahamic”) religions.

So if there's some essential core to what makes something an "Abrahamic religion," we're probably not going to find it. The myth of Abraham would be a contender, but as Hughes points out, Abraham is not used here due to his supreme importance in the three religions you list (Moses is arguably more important to Judaism, Christianity, and Islam). It's used to signal a "familial" heritage with Abraham (i.e. we Jews/Christians/Muslims are brothers with you because of our father Abraham). But Hughes (and other religious studies scholars) have pointed out that this is ahistorical and problematic in academic contexts. And the actual person of Abraham and his religion is not really helpful for answering your question, because scholars have questioned the historicity of the Abraham narrative in Genesis, and Judaism/Christianity/Islam are so different from what that would be.

So another way of taking your question is to interpret "Abrahamic" as being any religion that takes influence from either Judaism, or a religion that takes influence from Judaism (i.e. Christianity, Islam). If we're interpreting it this way, then the answer is yes. And some of them still exist! There are people who practice Rastafari, Druze, and the Bahai Faith. If you want to learn more about them, I definitely recommend looking up their current practices.

I could list more that fit this definition, but even still, the bounds start to break down. We run into problems like "What is enough influence from Judaism/Christianity/Islam to fit?" or even "What is a religion?" The latter refers to the slippery bounds of the concept of "religion" (William Cantwell Smith wrote a good book on this), but also the fact that it's not always easy to say where one religion ends and another begins.

For example, Greco-Roman religion and magical texts invoked foreign deities, and/or interpreted them as foreign equivalents of domestic deities. We have examples of pagans doing this with the Jewish Yahweh. Does that...make Greco-Roman religion Abrahamic? Again, one may retreat to finding some "essential core" to define Abrahamic religions so we can exclude Greco-Roman paganism, but many scholars would say this is a futile impulse. [Also, the point isn't that Greco-Roman religion is Abrahamic, but that "Abrahamic" may have to exist on a fuzzy spectrum that can't be sharply defined.]

But even if we can say "No, obviously Greco-Roman religion can't be Abrahamic. If there's one thing that isn't Abrahamic, it has to be that." There are still religions that you could still argue are "Abrahamic," even though the label doesn't really fit. So, there are religions that take our definition of having foundationally been influenced by Judaism/Christianity/Islam. For example, Sikhism takes much influence from Islam, such as quoting Islamic poets in its main holy text, and even referencing Adam in its holy text. However, I've never seen anyone call Sikhism an "Abrahamic religion." And whether Muslims or Sikhs call it one can have more to do with the non-academic interfaith motivation of "Abrahamic religions" that I mentioned above. American civil religion (cf Robert Bellah) has taken tremendous influence from Christianity. But is that an "Abrahamic religion"? And here again, the bounds of where one religion ends and another begins becomes a difficult question. We can see more problems with discussing history and culture with a word like "religion," which implies a certain amount of exclusivity and cohesion (the same applies to the Greco-Roman example).

However, there are religions that you could say fit our criteria, and could be seriously argued to be Abrahamic, in spite of rarely (if ever) being called Abrahamic. For some examples, Manichaeism takes a lot of influence from Christianity (Christ is one of the main figures in the religion). Yet, it's often seen as not being Abrahamic due to it also taking influence from Zoroastrianism and Buddhism. Yezidis practice a religion that is very much influenced by Islam, yet they are also often excluded from being "Abrahamic." And finally, Santeria is a religion that undoubtedly takes much from Roman Catholicism, yet it is usually categorized as an "African" or "African diasporic" religion.

So in summation, yes. While both the bounds of "religion" and the categorization of "Abrahamic" are a lot more vague than some might think, there are more "Abrahamic religions." Some are pretty uncontroversial (e.g. Bahai), while some would be more controversial (e.g. Sikhism). If what you want is a jumping-off point to learn more about the influences that Judaism/Christianity/Islam have had on other religions, then some good things to look up would be: Iranian religions, Gnostic religions, African diasporic religions, the early history of Judaism, the history of Judaism in the Greco-Roman world, and "religious syncretism" in general (even though that is also a problematic term).