In Christianity, there is the doctrine of the "trinity" of God. What would be the name of the corresponding doctrine if the number three were replaced with two, four or five?
To the best of my knowledge, owing to various heresies and schisms in the Christian faith we presently have the following forms of monotheistic doctrine:
Unity - Espoused by the Unitarians, who reject the consubstantiation of God and hold that He is strictly a single person. Jesus is regarded by Unitarians as a prophet who is not a part of the godhead.
Binity - Advocated by the Binitarians, who believe in the co-divinity of Jesus the Son and God the Father. What I find particularly interesting about them is that they believe Jesus was fully divine and co-eternal prior to becoming human, but that he fully surrendered his divinity while in human form, only to regain it in resurrection. This differs from the standard mainstream trinitarian view that Jesus the man was both divine and human.
So to make it really confusing, the Binitarians treat Jesus as a unity at all times, while the trinitarians see his human form as a binity. Still with me? :D
Trinity - The orthodox mainline Christian theology of the coexistent, coeternal three in one: Father, Son and Holy Ghost.
I am not aware of any further such terms of particular Christian significance, but there's a seemingly Scientology-like thing called the Hoffman Quadrinity Process that is all over the Internet and apparently in several countries.
If the Pope ever did pronounce the five-fold nature of God, I expect the word would continue to be based on the Latin root -nitas, and so following the pattern it would be quintinity.
Me, I'm signing up as an infinitarian. If the godhead has constituent parts, it's some unquantifiable number in one. An infinity.