Divinity: Original Sin Enhanced Edition multiplayer
Solution 1:
The gameplay is actually very well suited to coop.
You can solve the puzzles using several characters with communication instead of having to coordinate your 2-4 characters yourself
In town, you can do what you want. What I did in my coop playthorugh was to spend time in town reading, while my mate went around trying to steal stuff. Give yourselves 5-15 minutes after you completed the usual quest dialogues and buying/selling before going back out
Dialogues often give both players the chance to chime in with their own opinion allowing you both to roleplay. There is no lead character as there is in many other multiplayer capable RPGs.
There is is actually a mechanic to resolve conflicts between players. In many dialogues where both main characters are asked for their opinion, you can disagree, e.g. the first such example would be the shell at the beginning of the game where one could argue to keep it and the other to throw it into the ocean. If you disagree, you can then try to persuade your mate to see it your way using the speech skills (charm etc.), this then may end up in the persuasion minigame (the rock-paper-scissors thing). Eventually the action chosen by the winning player will be done.