Cuphead Online Here

There is no official "online" menu or matchmaking within the game itself.

To play "online," players typically use software that simulates a local environment by streaming the host's screen and sending the second player's controller inputs back. How To Play Cuphead Online Multiplayer | Parsec Blog Cuphead online

Although does not officially support online multiplayer, players have developed several highly effective workarounds to play with friends remotely. Officially, the game is designed strictly for local co-op only. Official Multiplayer Status There is no official "online" menu or matchmaking

By default, you can play as Cuphead and Mugman (or Ms. Chalice with the DLC) on the same system. Cuphead online