Probably the best way to do it is this:
You should already have an object "player" which is an invisible rectangle, and the "player_image" animations are stuck on top of that. If you don't have this, do it now, as it will save you a collision headache in the future.
Once you have done this, simply add and rename all of the animations in the player_image so you have something like this:
Then you can just add the corresponding other character's animations in the same format.
Then, you should have a global variable called 'character' or something which will always be the number your character is at the moment.
Then, in your animations, instead of doing
set animation to: "run"
you can just
set animation to: character & "_run"
And that should work nicely.