What would happen if Gen had to fight through DL's plot while technically alone, but having all the other Links (including all the sequel/OC/backstory Links for maximum chaos) stuck as voices in his head?
The others can try to take control by force if they want to, though if multiple people (Gen included) are trying to pull Gen's body in different directions he'll fall over or something from the conflicting feedback. He doesn't have access to the others' items but they can share knowledge and if everyone agrees to let someone specific have control that person's skills can be used.
...This is just Demise's problem but with Gen as the victim instead. Oh this poor boy.
Good News, the Links are not the sorts of people to hijack a body that isn't theirs, especially when the owner is actively driving it. Gen remains the pilot of his own existence for roughly 95% of the time.
For the other 5%, there are a few Rules in place:
Rule One, the Four are not allowed to drive, ever. Their multiplicity mixes very very badly with a single body. They accept this with a minimal amount of resigned sighing.
Rule Two, Gen's permission is required first, unless there is a legitimate emergency and there's no time for permission.
Rule Three, in the case of said legitimate emergency, Lore drives. He has the most experience with Weird Possession Situations.
On the other hand, they never quite got around for making Rules for the rest of it, such as taking turns talking or whatnot. Gen hasn't had a single second of quiet headspace since this whole mess began, and it he hasn't gone a little bit mad from the mental cacophony of it all by now, then he most certainly will have by the time this whole mess ends