In all Pokemon versions, you'll face doing a Two on one situation. This gave me the idea of a 2v2 competitive battle against other players, allowing teams to be created making more social activities and more strategic plays. It will also help the economy stable due to people buying supplies needed for the battle.
My idea of how to implement this into the game is by making an area/building where Duo's can take part in and having an invite option that will create the party. Once the other player accepts your invitation you can start matchmaking with other teams. Maybe you can go for a nice friendly match, or enter your team into a tournament which uses a ladder structure that 8 teams need to battle through for the grand victory.
Allow teammates to use potions and heal one another pokemon/ cure them.
Stunning a player's pokemon for the other to attack.
Trying to use a Pokemon "Type" combo strategy. (Type meaning... fire, water, normal, ect)
I think this would be a really fun idea to add to the game, making it even more competitive and strategic.