Super Bomberman R’s official website has laid out details for the multiplayer options the game has to offer.

Fpr local play, you can have up to eight controllers paired with the Switch for an 8-player battle. However you can also pair two controllers to four Switch systems to  play with eight players, so you don’t need to only do it one way,

For the online play,  you  are able to pair two controllers to four Switches connected to the internet, and then participate in an 8-player battle that way as well.

Source

.