How can I handle a PC wanting to be a “twist” villain?

My group has been following a premade campaign that has a decentralized plot structure that relies mainly on adventurers "finding their own adventure". This means that while the campaign provides ample worldbuilding information and premade side-quests, the campaign has no clearly defined antagonist or central plotlines. Normally, in a group focused on exploration and combat this wouldn’t be a big deal, however in my group there’s been a general feeling of dissatisfaction at the current lack of plot progression, as well as the lack of a main antagonistic force.

In order to help develop a centralized plot, one of my players recently came up with the idea of his PC secretly acting as a twist villain. The basic premise is that they would conduct certain actions between sessions in secret (i.e. assassinating certain NPCs, instigating strife between factions, etc.), such that the other players would have mysteries to uncover, as well as a means of driving change in an otherwise stagnant story.

In order to prevent the player from gaining an unfair amount of agency and spotlight, the following would be enforced:

  • The PC will not become "the BBEG". That is to say, they will never become the primary antagonistic force in the story. They will never work fully in opposition to the other PCs, but will follow goals that the other PCs may view as acts of evil.
  • The PC’s villainous acts will serve to develop a larger storyline. The PC will only be privy to information pertaining to their own actions; the player of said PC will not be aware of the overall direction of the story.
  • The player has agreed to relinquish control of their character to me (the GM) in the event that cooperation between them and the rest of the party becomes impossible.

I’ve heard that PVP generally has a negative connotation and I have some concerns with the idea of a player having an elevated degree of control in the storyline, mostly related to spotlight issues. However twist villains appeal to me and I think that the other players will appreciate the resulting narrative shift.

RPG.SE has a vast array of experiences and I’m certain that this scenario has occurred before. I’m hoping to draw on that experience to help answer the following question: how can I handle a PC wanting to be a twist villain?

  • What steps can I take to ensure that this doesn’t come across as an act of favoritism?
  • How can I prevent this from turning into an instance of "My Guy" syndrome?
  • Are there any pitfalls of this choice that I may want to avoid?

Preferably, I’m interested in answers that ensure that the mystery surrounding the villains identity is preserved, while reducing any potential in-real-life strife.

Contextual points to consider:

  • The group has historically responded well to story-driven adventures. Roleplaying abilities are generally strong and players expect the presence of heightened drama.
  • When we started this campaign, we were aware that the campaign was more open-ended than others we’ve played in the past. It was selected as an experiment of sorts; needless to say the experiment has proven somewhat unsuccessful and everyone involved is aligned on the fact that the campaign requires a stronger storytelling backbone in order to remain interesting.
  • Session Zero has already occurred and this sort of behavior was never fully discussed. Players are aware that their PC’s goals will not always fully align, and that PVP may occur, but we haven’t discussed the possibility of players being fully villainous.
  • Players are aware that they may receive more or less narrative attention based on their choices and the direction of the story.