Welcome to the forums @RastermanVector!
How are your animations setup? Are you using bone-based animation, frame-based, or something else? Also, what perspective does your game use? Top down, side-scrolling, etc.
If this was a 3D project, I would suggest using animation blend trees to handle this, perhaps with IK to handle the arms of the character boosting the other character. For 2D, I would look at trying to "fake it" when you can, perhaps by requiring the characters to be in certain positions or facing certain ways before transitioning, so that way you can better control the transitions.
Then, if the animations are separate the entire time, you can just have the position and rotation of the boosted character follow the other character.
If the animations are the same, I would start the transition animation and then hide the separate character once they are boosted, disabling the code and other stuff so it doesn't get in the way. Then when transitioning back to two separate characters, I would play the transition animation, move the hidden separate character into the needed position, make the separated character visible, and then enable the code and other stuff.
At least, that is how I would approach the problem based on what I know. Hopefully what I wrote above is of some help!