When all progress says "your relations are too depraved" or just "drained", what exactly am I supposed to too for further progress?
For the events that say either of those things, you cannot progress further at this time, so don't bother repeating them, move on to other things.
When going on the progress tab, some characters do say "Maybe you raised allure to maximum. Still, there may be more naughty events". As well as "There are still can be opportunities to raise sexual tension".
This means there is still an event with this character that you haven't found. You have to try other things. Unfortunately, the hint system is the real weak point of this game.
But even after doing the same scene 10 times, nothing changes, all relation improvements seem to have stalled, while relationship can still lower.
Stop doing the same scene after you see "drained" or "your relations are too depraved" you need to do something different or it can mean you are at the end of the character's content if you don't see the message about "...more naughty events" or "...opportunities to raise sexual tension."
Is it possible to ruin your game by advancing too much? Or am I just missing something? Maybe I need to advance another storyline further to have progress?
There are occasional bugs, but I don't remember a case where it was possible to break the game by advancing too far, at least not that was ever disclosed. Yes, you may need to advance another storyline although those types of dependencies are rare. Most likely, you just do something very different with the character. Sometimes, the things that trigger new events are obscure, and worse, sometimes they trigger randomly.
