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No. At this time, the only thing you can do is set a couple of rules regarding the clothing your submissive wears. I think the only two options are to always wear tight clothing and to never wear underwear

In my current playthrough, my fellow students see me "as extremely exhibitionist, very promiscuous, and pretty studious." Not sure if those are the only three reputation characteristics or not at this time.

As far as reactions, they seem to be somewhat limited at this time. Some of my fellow students do call me a slut while others will comment that I never wear underwear while using a pencil to pull up my skirt.

Regarding my grades, so far only the Cheerleading coach has mentioned that she has heard that I'm doing well in my studies.

After you finish the D&D campaign, you'll ask the Admirer out on a date. The date ends his designated arc.

Also after the end of the campaign, you can talk to the Admirer's Admirer (the one who gave you a lot of grief during the campaign) to discuss the problems between you. This can result in a change in your relationship with him.

Right now, there seems to be three characteristics that affect Reputation: Exhibitionism, promiscuity, and grades. In my current playthrough, my fellow students view me "as extremely exhibitionist, very promiscuous, and pretty studious."

Would it be possible during Halloween week to allow male characters to wear their bought shirtless costumes in all buildings?

I bought the Barbarian outfit. While I was allowed to wear it to the Halloween party itself, I wasn't allowed to wear it to class or in any other buildings since the costume doesn't come with a shirt. Seems like a loosening of the rules would be okay for Halloween week.

When you clock out of work, the text on the screen will give you an idea if you are close to a promotion or not. If you are, it will say something like you  need to work a couple more shifts. If you are not close, it will say you need to work several more shifts before you can be promoted.

In addition to what Bun33y said, there are a few occasions where you might get two people to approach you for a threesome. I've had it happen working at the River Rat and being on the Cheerleading squad.

In addition, you can initiate a threesome (or even up to an eight person orgy) if you have submissives or are in a polycule relationship through the Date or Hang Out texting option.