You might be thinking of Cybele, the Great Mother, who was a common mother goddess of the Near East. She was associated with Artemis, Leto, and others, including often the potnia theron or "Queen of the Animals." In iconography, she often was depicted as having many breasts.

During the 2nd Punic War, the Romans received a Sibylline oracle that suggested they would never win until they had brought the Great Mother of Mount Ida (in Anatolia) to their city. They then interpreted the oracle to mean the Great Mother at Pessinos, which was a huge black stone. They asked the local power, Pergamon, if they could bring it Rome, and were given permission. Livy (29.14) relates how the rock, or part of it, was brought to the city and set up as a cult object to the Great Mother.

Alkibiades415 already has you covered for perhaps the most famous instance of Romans taking a deity and bringing it back into the city, but what I'd like to do instead is look at the broader picture. We know that this isn't an isolated incident: the temple of Juno Regina on the Aventine, for instance, supposedly had a wooden statue of the goddess from Veii brought by M. Furius Camillus after he conquered the city (see Dionys. XIII.3, Plut. Cam. 6, Val. Max. I.8.3). This is a particularly helpful case study, as Dionysius tells us how that happens: it is worth quoting the passage in full.

'This same Camillus, when conducting his campaign against Veii, made a vow to Queen Juno of the Veientes that if he should take the city he would set up her statue in Rome and establish costly rites in her honour. Upon the capture of the city, accordingly, he sent the most distinguished of the knights to remove the statue from its pedestal; and when those who had been sent came into the temple and one of them, either in jest and sport or desiring an omen, asked whether the goddess wished to remove to Rome, the statue answered in a loud voice that she did. This happened twice; for the young men, doubting whether it was the statue that had spoken, asked the same question again and heard the same reply.'

Note here that Dionysius is writing a considerable time after the event he recounts (the conquest of Veii happens at the start of fourth century BC, while Dionysius is a late first century BC author), but his attitude is at the very least telling as to give us an indication of how Romans of the first century thought about the relationship between a divinity and their city, and about Roman imperialism. What seems to emerge out of this text - and other examples - is a highly localised character of Graeco-Roman religion, centred around a relationship between a deity and their city. The Romans then systematically seek to disrupt this relationship and re-route them towards Rome and its spiritual world: and it is not exactly something new, as this is precisely what Greeks do as well (one just needs to consider the case of Aphrodite of Aphrodisias, who seems to be local deity consciously re-interpreted by the Greeks as Aphrodite). Note also that evocatio or calling out of the gods, was a common tactic in Roman warfare. It helped to raise the morale of the enemy, and later helped with the unification of former enemies: this might also explain why gods are targeted. In the narrative, Camillus is essentially trying to persuade Juno that if she chooses to 'pick Romans' instead of the people of Veii, she will get better treatment along with a fancy new temple: and apparently, it works.

I hope this brief sketch serves as a short introduction to this topic, which is extremely complex, interesting and allows one to think about a lot of issues from the materiality of the Roman world to origins of their pantheon or perhaps the way they approach imperialism. From memory, I believe you can look into Juno Sospita as another similiar case to the one I described.

As an introduction to this topic, I would recommend 'Religions of Rome: Volume 1, A History' by Mary Beard, John North and Simon Price from 1998.

On the role of foreign gods in Roman success, see Eric M. Orlin, 'Foreign Cults in Republican Rome: Rethinking the Pomerial Rule' in the Memoirs of the American Academy in Rome Vol. 47 (2002), pp. 1-18 (18 pages). This author also has a book called 'Foreign Cults in Rome: Creating a Roman Empire' - I haven't read it, but seems useful for you.

On Juno Sospita, see 'Juno Sospita and Roman insecurity in the Social War', in Celia E. Schultz, Paul B. Harvey, Jr., 'Religion in Republican Italy', Cambridge, 2007.