Can you play multiplayer with mods?

[SoDI]

[Outcats]

Yup! Most mods let you play online without any issue, though if its like a skin change people in MP won't see the changes. Any quest mods won't be accessible to people without the mod either.

[Ember]

There is no ban system if that's what you're worried about. Go nuts with the mods. Just make sure you don't ruin anyones experience with them.

[CookedMeat]

If you're worrying about legitimacy, using Mods in multiplayer won't get you banned, but do beware not to negatively affect your teammate's experience.
If you're worrying about compatibility, I'm pretty sure most Mods author will provide the information at the download page.

[SilverCuppedRamen]

You can, just make sure to play solo if you install mods that affect damage numbers to unbalanced levels.

[Mr. September]

Should be alright as long as you don't bother anyone else. Dropping this here in case you find it useful:
https://steamcommunity.com/sharedfiles/filedetails/?id=2359218616
Happy modding and have fun!