I've just finished a normal mode playthrough as a duo in co-op. Was such a lot of fun, we had a real laugh throughout.
Combat is so much fun multiplayer, but the story doesn't adapt for it. So you have to accept that whoever initiates the conversations or encounters will drive the story. We discussed important decisions on Discord, so it was ok. But I could see this getting messy in 4-player depending on how well the players know or trust each other.
Also the poor ending is even worse in multiplayer. In solo it is unfinished and unpolished, but co-op takes this to another level of awfulness. Because I wasn't the one initiating the cut scenes, my character was totally invisible throughout the entire ending of the game, not represented even once in any of the cut scenes or dialogues, not even standing in the background. It was as if my character had never existed. That's an huge design flaw they absolutely need to fix.
Both of us agreed on finishing that the ending was a total let down and left a lasting sense of disappointment. Which is a crying shame because of how amazing the rest of the game was. But a bad ending stays in the memory (Mass Effect I'm looking at you) so I hope they patch in a much better epilogue.