Physically, your character is only capable of carrying a party of 6 at one time even outside of events. This means if your character goes out, someone has to stay home when they have more than 6. (This is actually a Pokemon mechanic!) You can have more than 6 total Pokemon, but you will not be able to participate in any of the current event if you are utilizing other Pokemon so leave them at home. As stated in the post, the PokeBit will only register current event Pokemon.