Just for anyone's future reference, how would you make a trainer (Or two trainers) engage you in a Multi-Battle?
If you don't know what I mean by Multi-Battle, I mean a battle where you fight with another person on your side. You use three Pokemon from your team of 6, and the same with this other character. Marley in Victory Road is an example of this, but without you choosing three of your Pokemon to use.

It wouldn't be a common thing, probably reserved for a Gym battle or something.
Let's say you have another character with you (Not shown in the overworld, since you can't have an NPC following you in Gen 3 without some tedious Rom Hacking Magic) and you face this trainer (Or two). When they challenge you, the menu for choosing your three Pokemon will pop up, and once you choose, the battle will start. The other character will send out their Pokemon to battle with yours against the trainer(s) who challenged you.
Does any of what I'm saying make ANY sense?