@Megalomaniak thanks for the insight. I'm not sure It completely relates to what I'm trying to pull here - we're not looking for the Brute to hold the Runner (let's call them that), but for the Runner to be on Brute's shoulders.
Just to add some detail for better understanding (this thread might come in handy to someone trying to do a similar thing): We're triggering the "enter" animation when X positions of the two characters meet and then upping the Ypos of the Runner to be in the correct position relative to the Brute. There is an aiming mechanism involved for the throw.
The exit animation is actually the Brute reaching with his hands and throwing the Runner. I still have to figure out how to achieve this for it to look fluent. Animating the enter animation (climbing and sitting on shoulders) can be done by utilizing what @TwistedTwigleg advised - having the Runner going behind the Brute, hiding the individual Runner sprite and adding him temporarily to the Brute's animation. The throw is still something I have to figure out, I'm probably going to have to think of a similar trick, but in my head, this is still not working.
Btw, my inspiration came from Donkey Kong coop, but I'm looking to incorporate it in 2D (In DK, even the old ones, this was done in 3D). Although doing this in 3D is an option, it's something I'd rather not do because I'm not that versed.
Here's a quick sketch of mine so you can visualize what the "Merged" mode is supposed to look like in terms of composition.