If you have to exit and select (as opposed to meeting conditions or button combo in the game) this sounds like something more in the world of character select cheats and they don't always work in battle (might work between rounds though). Where they tend to work better is in games that allow you to select two characters that allow you to tag in/out or jump in when the other is killed. That said games on 3d systems can be better for this than more classic 2d stuff.
Such cheats are among the more basic ones out there but not necessarily what I would learn with in an ideal world. The principle is the same though and you select different characters, search to find what is chances between them (possibly with savestates, do note that some selections are merely hovering over it in character select, some when you press the confirm in character select and some only when all players have selected a character and confirmed it).
I don't know what we have for PSP cheat finding guides but the principles are much the same everywhere so
You would then presumably make button combos to select specific characters or cycle round the values you want.
If you are going to attempt it as a more general hack then ignoring the cheat option that is one of the more advanced hacks most would reasonably attempt as you will be speaking to something quite fundamental in the code, possibly to the point of having to guide it through loading new models/textures/animations/move sets. If there is a character that copies move sets or can transform in game to mimic other characters (many games of this era and a bit earlier tended to have one of those, even if only as a boss) then that might provide you an easier option.
