Question about joining a faction (Outward)

We play with a friend in a co-op and the question arose that we could not find on the Internet.
There are factions in the game, for magicians, warriors, etc.
My friend is a magician and he needs a faction for magicians, but I am a warrior and I need such a faction, the question is, can we join different factions in a cooperative? Or if one of us joins one faction, the other will be considered in the same faction and will not be able to join the desired one?
The question is much shorter: can I join the faction I want if my friend has already joined another?