Sounds fun! Adjusting the battle mechanics would probably be the largest undertaking.

my idea for it is
currently you fight 1 (your pet) vs 1 (enemy)
- if your team has 2 pets, then 2vs2 battles could additionally appear. 2vs1 battles still possible. Story specific / scripted battles will need difficulty balancing (make them harder so that having more team members won't render these battles too easy).
- if you send out a team of 3 pets then same logic as above applies. Now 3vs1, 3vs2 and 3vs3 battles can possibly appear randomly. Scripted battle difficulty needs balancing.
- same for a 4 member team. 4vs4 battles get added. Scripted battles are the most difficult in this mode.

in 2, 3 and 4 member teams the battle system will need to include a visual guide of the turn order. Aka, which team members / enemies will get a turn to act when based on their speed stat.