How do I rig a sprite skeleton with a sprite sheet?

I'm attempting to recreate Yoshi from Yoshi's Story and a few characters from Vanillaware games in unity but the task is proving impossible so far.

In this example sprite sheet, multiple 'sprites' would correspond to a single bone, but unity seems to only have functionality for one big 'sprite' to have all of the necessary limbs already on it. Is there a way to connect individual sprites together and NOT have to seperate them into multiple sheets?