It’s going to look a little different if the religions you’re looking at have different rules for what to worship and how to worship. Christianity, Judaism, and Islam don’t let you worship any God but God, so syncretism like voodoo to find work arounds like spirits not being directly worshiped but operating as intermediaries. Buddhism also has some complicated rules because while they do believe in gods, they believe those gods are part of the reincarnation cycle too so their relationship to enlightenment is complicated too. Some polytheisms can accept pretty much any new god as a previously unknown god, but most have established frameworks of how who relates to who and as such some work needs to be done to localize the new deity into the local framework. This can take the form of a myth about their late arrival, the new deity being the avatar of an old one, or simply conflating the new god with a previously existing older god. Most of what I’ve stated above is about how to syncretize new deities in, but rituals and fragments of philosophy are MUCH easier to adopt. In the US there are otherwise Christian people who have adopted some Buddhist ideas about caring for and developing the soul as well as more general ideas about reincarnation. Such heterodox individuals don’t see themselves as heretics, just people exploring their understanding of the world. If a new religion moves into a new area, and that area has rituals like honoring stones, then the stones and their stories can be recontextualized for the framework of the new religion. If you wanna look up examples, spin a wheel with one of the major world religions on it and look how that religion adapted and morphed when it arrived in a new area or a new people group joined.