Yes. It happens a lot in local junior football. When I was a referee a few years ago there was a rule in the local leagues- I think it was an FA rule- that if the official referee didn't turn up or the league had no referee available, the the officials of the clubs involved in the game had to agree on a referee between them. Sometimes each manager took half the game, although that probably wasn't really allowed as I think it's supposed to be the same ref throughout for consistency