Personally, I'm not convinced the club is the best approach. A simple continuation of the Mall wouldn't be different enough to distinguish itself from Corrupting Kayleigh. One of the criticisms of CK was that it was very linear when compared to Unforgettable Dinner, and if the Club's gameplay is only a series of tasks that result in either a) Game Over or b) Continue on to the next task, I think the game could flounder.
I also don't think it's very interesting if Kayleigh is corrupted into a sex toy like Amanda. Simply saying yes to everything stops feeling like corruption and feels almost uninteresting. Do you do group sex? Yes. Do you do anal? Yes. Do you do other women? Yes. Do you do double penetration? Yes. Do you do BDSM? Yes. Do you do voyeurism? Yes. Do you do A2M? Yes. So on and so forth. Eventually it just isn't interesting because there isn't a character there, just a sex toy.
If the Club is going to happen, then I would suggest the player be able to customize their Kayleigh. I think all players would have her continue her corruption, but I think it could make for more engaging gameplay if players are able to say yes or no to a task without a game over. Maybe that could roll into various endings that reflect Kayleigh's level of corruption. Say "yes" to everything? Kayleigh becomes a mindless sex toy for Edmond. Say "no" to everything? Kayleigh holds on to her independence but doesn't explore any of her interests. And then shades of gray in between.
But really, I worry that the club is a dead end. Too similar to Corrupting Kayleigh, and with a questionable narrative drive. What is Kayleigh's motivation? How much can you really be corrupted in one night at a club before it feels forced (from a narrative perspective)?
Instead, I would start from scratch. I would take Kayleigh as she exists at the end of CK and build a new story around her. New characters, new setting, and a central plot that doesn't exist singularly to advance her corruption. She can become more corrupted in the game, but it would be a biproduct of other events taking place around her if she chooses to go down that road. I would also allow the game to be set over a longer period of time instead of one night, or a day or two like in the case of CK. Building this new game off of the events of CK would help avoid a common problem in female protag games. Too often in female protag games, the MC starts off far too conservative; it makes advancing their story and/or corruption cumbersome. Get the balance wrong and the corruption feels unearned, get int wrong in the other direction and the game feels unrewarding. Starting Kayleigh off already corrupted could make the early game much easier on the dev team (look at a game like A Wife and Mother for how a slow burn can go off the rails). Not only would we avoid the problem of a MC that's too conservative, but we would make use of the world building that was accomplished in Afternoon, Unforgettable, and Corrupting.
If I were to spitball an idea, it would be something like the following. After the events of CK, Kayleigh is flush with cash; but her personal life is in shambles and she's aimless. While she and her mom are now financially secure, they are far from wealthy; and there have been consequences. Jen is a mess since the events of CK, simultaneously relieved to be free of immediate financial burdens while also distraught over what she "allowed" her daughter to do. Meanwhile, Kayleigh's father is furious at the incident, and her brothers are disrespectful of her and jealous of the money. The central theme of the game could be something like Kayleigh trying to find her footing in this new world. She can either take the money she earned and put it to good use, maybe rebuilding her reputation in the process, or double down on her new found sexual confidence and explore her limits.
It wouldn't necessarily be structured in a sort of Good/Prude vs Bad/Slut choice, because I hate it when making the "good" choice clearly limits a player's options for fun sexy content. Instead, I think Kayleigh would explore her sexuality on both paths, with pros and cons on either side of the spectrum. Either way, a new game like this would give Kayleigh far more agency over her continued development as opposed to yet another game of taking orders for money from Edmond.