I see sidekick just as nemesis, a custom persona to use in specialized arc stories.
No need to make him a pet.
Here is a train of thoughts to integrate a sidekick/nemesis system :
You meet your future sidekick on a mission. He is a newbie and completly neutral (not hero or villain) but inspired by you and would like to follow you in your adventures.
With arc stories involving him, you lead him to the path of goodness or corruption (just like tip missions).
option 1 : you push him to far in the opposite direction. That will lead to an arc story with a morale clash and he himself becomes your nemesis.
option 2 : he is aligned with you. He will be defeated or killed and then becomes possessed by an evil being that will make him your nemesis.
And since he knows your weaknesses, he will hire goons with appropriate means to deal with you.
That would lead to the equivalent of Quantum NPCs but specificaly for you.
Since the mecanism exists, it should not be that complicated to put them into random missions (like for Kheldians).
And further arc stories can take place after that.