I played every route and unlocked all the gallery manually (this game was basically my only source of "material" for the whole week and a bit) and I can tell you that you don't get any events at night that aren't related to either Chika having the Lewd status, or related to triggering certain day-time events that then have consequences at night.
However, if Kazuki just works and Chika isn't in Lewd status, nothing happens even if you maxed out events with one of the guys, including their 3 special events that max hearts that require items.
So yeeeeeaaaaah. No. It doesn't get better with any of the other guys, though some of them have more or less night or day events where there's pixel art of Chika that you can see. I think it's Saruyama that has the most events that extend into nights? But he also has the most annoying event conditions too...
He has two events that can only happen on a Sunday, and I think both specifically require taking Chika out on a date. The events are hot, sure enough, but depending on specific week days like those on a time limit makes them annoying.
I haven't tried to see what happens if you progress more than one guy a lot. With 40 days, I THINK you can max out the hearts for two of them, depending on which you try with and how... but I don't think I'll bother.
In any case, when it came to that last thing you mentioned. Well, read the spoiler if you want.
You basically get something like that with Saruyama's ending, where Chika fucks both of them. She ends up still loving Kazuki and being addicted to Saruyama's dick. She loves Kazuki more, but her desires are more satisfied by Saruyama, and she's basically with both of them. Kazuki concludes that it's fine as long as Chika's happy, and the two guys compete in various ways to keep her satisfied.
The Janitor ending implies that something like this may happen there as well, since Chika's relationship with the guy is more like that between call-girl and client, and she invites Kazuki to keep fucking her whenever he wants when he sees the truth, and the janitor doesn't mind. Even in the store ending, Chika comes back home and it's left on a note where Kazuki could indeed keep fucking her even as she becomes an AV actress.
The only ending where the "bull" seems to truly monopolize her is Shota's ending, who seems to have no intention of sharing Chika with anyone, and the two form a twisted relationship where Chika is technically his slave that does whatever he wants... but she also manipulates his libido into satisfying all of her overwhelming urges. Yes. The shota is the biggest bastard in the whole game. XD Even there, Kazuki awakens to his inner cuck and enjoys the greatest masturbation of his life so things don't end up particularly bad for him.
In any case, it's not surprising that things ended up like this with the game being as it is.
I agree with you that the game could have had Chika do various things during the day and evening, which could be influenced by her stats as well as the schedules of the other guys after her. There's a reason why I consider Nebel the best NTR game currently out there, because Kana and L do things all on their own, and all the player can do is prevent them from happening or not, but he can't control their events directly.
This game technically had the potential for something like that too, with things being pushed around some depending on how and when the player pays attention to Chika and her nymphomania.
However, at the end of the day, Acerola has no experience with games where a main character is basically programmed to do things and whatnot. Even in Monica, any night events of Monica's are dictated by event progressions and whatnot when you choose to enter the cuck's part, while the other two girls have very simple patterns that were also dictated by events progressions in certain ways.
I have no idea if they even understand the appeal of something like that. XD If you looked at ci-en posts and whatnot about some of their NTR games, their focus seems to be on the girl and whatever slutty stuff she got into, the cuck seems to be more of an afterthought because it's NTR.