Steam controller metadata
Valve's app data reports controller_support as full. That confirms the store-level support category, not guaranteed compatibility with every third-party device.
Local controller setup
Connect inputs before entering Local. One keyboard-and-mouse player can join three controller players for a four-person couch group.
On Steam Deck, Valve notes that an external controller may need to be selected manually as the active primary controller.
Frequently asked questions
Does Machine Party have Full Controller Support?
Yes, that is the current Steam metadata classification.
How many controllers work in Local mode?
The v2.0 notes say up to four.