These branching stories are going to have 3 very simple premises: 1 You exist in a world where your character AND ONLY your character gets to have sex with whatever group or groups of people you choose wherever and whenever he or she desires.
A lucky protagonist stumbles across a magic book that lets them rewrite the rules. A magical lamp finds it way into some world or another, whether the "real" one, a fictional one, or even just one completely made up by the writer.
It is either empty, or already contains a sex genie. A sex genie, much like normal genies, grants the wishes of the one who holds their lamp, but unlike normal genies, they are limited not in the number of wishes they can grant, but in the kind of wishes.
In short, they can grant an unlimited number of wishes, not just three, but the wishes must be sexual in some way. Furthermore, the sex genie inside the lamp should be completely loyal and dedicated to their Master, or Mistress, loving them unconditionally, and lacking any desire to ever say no to them.
If the lamp arrived in the world in question empty, it will suck in the first person to rub it, infusing said person with its power, and rewriting their mind to be completely submissive. It is in a genie's nature to serve. If the lamp already has a prepackaged genie, then the one writing the story can come up with their name, gender and appearance. Welcome to an alternate reality that's a patriarchal paradise - where humans are hypersexual beings, public sex is normal, misogyny runs rampant, and women subsist entirely on semen to survive!
