Since this quest system can't be implemented due to how the homunculi were designed, I figured there's nothing wrong with sharing what ideas I had in mind for it.
Or how about homunculus leveling quests? (If it's possible to script quests to only affect homunculi.) Develop a quest system like Pokémon where you can have your homunculus do kill quests and be the very best like no one ever was!
Based on the Pokemon RPGs, this quest-leveling system would encompass NPCs scattered throughout Midgard that would "challenge" Alchemist-class players to homunculus battles.
Alchemist players must first register for the "Midgard League" in Aldebaran at the Alchemist Guild HQ. From there, Alchemist players can then seek out various Alchemist class NPCs to battle their "homunculus" (the NPCs would each summon 1-6 different monsters as their "homunculi"). Successfully defeating the NPCs would reward EXP to both the player and the homunculus and loyalty bonuses to the homunculus specifically.
Not sure how to structure gym leader-type battles, but those would summon either MVPs or boss monsters as their "homunculi."