Hey there, just had an idea that might be cool.
Additional tournament mode. Hear me out.
So it starts the same way essentially, everyone has 4 lives and is trying to win by building the best team. Only there is no win cap. Instead your are ranked based on how many wins you've gotten, and your team and win/life amounts are saved even when offline much like your achievements. That way you can come back online and fight again. You can only fight people with the same amount of rounds fought just like the standard game, meaning if you are in the lead you cannot fight until someone battles their way to you. They can fight your team while you're offline, but it only impacts their score and not yours.
You might be thinking that it would get really broken because of people using balls of ice and pickleballs to power up their team, but that is okay because there can only be so many people at the top and eventually someone will do it better and take top position. This will restructure the top entirely each time because now the old best will lose to the new best and have to restart and restructure their team.
Okay maybe that would be dumb, just brainstorming a bit.