Can I play with mods in multiplayer?

Yes! But: All participating players (in case of Coop mode all 16 players) have to use exactly the same mods and the same versions.
If you have problems, just copy and send your mod folder to all other players, then it should be exactly the same ;)
In addition, faulty mods can cause problems, even if there is currently no known mod that causes problems in MP.
To avoid this you can deactivate the activated mods one by one until the game starts again without errors. After that you can switch them on one by one again and leave out the troublemaker. If it still does not work properly and no other error can be found, please send a message to the mod creator, so that the error can be investigated and fixed.