Is the general answer a simple "we don't know", or "we have no idea", or is there any reason to believe specific places, like a hypothetical specific unexcavated archaeological site might have one but we don't have the means to excavate them yet? (perhaps because some city was built on top of an older library that may contain important writings, and so we can't excavate, etc...)
It’s very possible that there are things like that we haven’t discovered yet, that’s what makes archaeology so exciting!
New sites are being discovered all the time, such as the mosaic of Achilles recently discovered in a farmer’s field in England. The mosaic wasn’t created in isolation—who knows what might be hiding in the area if the owners were to let the whole field be dug up?
Unfortunately, as you mention, not everything is as simple as excavating an open field. An example I like to bring up is Alexandria in Egypt which faces quite a few problems when it comes to this. First, the modern city is built directly on top of the Ancient one which makes it immensely difficult to find enough space and money to dig it up. The Citadel of Qaitbay was built on the ruins of the lighthouse and is in and of itself an object of important cultural heritage so the chances of a lighthouse excavation are nothing.
Another problem is that much of the ancient city is currently underwater, and would take an immense amount of time, effort, and money to make accessible. In recent years, the city has taken a great deal of interest in these underwater sections and made a big announcement for an underwater museum several years ago but have yet to actually do anything.
So, to answer your question, a huge possibility. There could be a manuscript containing the entire rest of the Iliad [edit: see my reply below for what I actually meant by this] lurking somewhere. The trouble is actually getting to a point where you could find it.
It is very unlikely that entire epic poems or other complete texts are lurking somewhere undiscovered, though not impossible. Ancient people largely used papyri or parchment scrolls, both of which are susceptible to degrade over time except in dry conditions. This is why so much papyri was found in Egypt. However, even the papyri found in Egypt were largely take from ancient "dumps" placed in a desert and were already fragmentary in nature. Practices of antiquities dealers like cutting up papyri or separating pages of codices to turn a higher profit also don't help this situation because manuscripts that were once larger or more intact are often separated today. Additionally, in the period when many papyri were initially excavated, the tactics were more "hit and run" than scientific, largely because, in addition to lax archaeological and cultural history standards, they were working against a rising water table (that would destroy the papyri) and the practice of harvesting sebbakh, a rich mud used for fertilizer in Egypt's exploding agricultural industry of the late 19th/early 20th century. Sebbakh was often found near archaeological ruins (which probably helped it be so rich) and was the type of soil in which papyri were often found. So while papyri fragments can still be found in Egypt, much of the material may have been destroyed even in the last 100 years due to environmental conditions and antiquities trafficking. There are certainly fragments of literary texts hiding in the huge collections of papyri in institutions and private collections around the world; usually the "flashiest" pieces are identified and published first, but there really is quite a bit of material to get through a limited number of people able to decipher these texts. So all in all, small pieces of ancient texts might be found, but it's unlikely that we find an entire collection.
It is true that archaeological methods are always improving, like with the Herculaneum scrolls. Techniques to read these charred papyri have allowed people to get at the texts without completely destroying them. That library mostly contains philosophic texts, not any epics. Another famous example from outside of Egypt are the Dead Sea Scrolls; these texts were mostly Hebrew Bible and Apocrypha. Both of these examples are from extraordinary archaeological contexts, one being the volcanically-preserved Herculaneum and the other being the Qumran desert caves. You are right to point out that many potential archaeological finds have been built over by succeeding generations. This is why the city of Rome has such a slow time of expanding their subway system--every time they dig to expand, they stop to consider the archaeological finds. So while there is a lot to be found under modern cities, it's not yet possible to unearth that material without a lot of destruction. Even if modern scholars could fully excavate anywhere they like, it's important to remember that the environmental strains of being under settlements (water, sewage, etc), in additional to the local weather, make it unlikely that fragile items like papyri or parchment would survive. Even if they did, it's unlikely they would survive to reveal anything in its entirety.
Sources
Davoli, Paola. "Papyri, Archaeology, and Modern History: A Contextual Study of the Beginnings of Papyrology and Egyptology." Bulletin of the American Society of Papyrologists 52 (2015): 87-112.
Sider, David. The Library of the Villa dei Papiri at Herculaneum. Los Angeles: J. Paul Getty Museum, 2005.
Bagnall, Roger, editor. The Oxford Handbook of Papyrology. Oxford University Press, 2011. Especially Timothy Renner's chapter "Papyrology and Ancient Literature"