https://www.team17.com/overcooked-2-faq/overcooked-2/
How many players does Overcooked! 2 support?
Overcooked! 2 supports up to four players in either local or online play. On Nintendo Switch, we also support wireless multiplayer for up to four players.
With up to three local players sharing a console it is then possible to also play with other players online. When two or three players are in the game locally, online friends can search for and join the game, or other players can join online through matchmaking.
Are there any limitations to online play?
Several configurations of online players are possible but, due to limitations around the online system’s ability to merge parties, the game does not currently support 2+2 online – that’s two players on one console and two on another. This is something we would have liked to have been ready for launch but is a complicated undertaking and, as such, will take much longer to be ready. Please look out for a post-launch update to introduce this feature at a later date.