If you want high levels of interactivity, I can recommend Ravager, Third Crisis and Seeds of Chaos. All three are substantially more interactive than the Headmaster. Third Crisis also has the bonus of being completely finished.
Fair warning, though: all three also go hard on the kink (yes, more so than the Headmaster). For some reason the more interactive games also tend to be the ones with the more extreme kinks.
I can also second Rusty's recommendations of Corrupted Kingdoms and Harem Hotel. That said, the interactivity in Harem Hotel is kinda fake interactivity. You can move around and choose what order to do things in, but ultimately everything plays out almost exactly the same no matter what you do. And Corrupted Kingdoms is somewhere between that and the three I listed above.
Eternum, Once in a Lifetime and Ripples are all good games but are traditional visual novels - you make a few choices here and there but there's not a ton of interactivity.