I recommend
Roundscape (Fantasy) and
Uprising (Superhero) by the same creator. They're both heavy story-based games but are less VN-like than your hints. Roundscape is still in development but has more content while Uprising was abandoned but still has some good content.
If you're somewhat interested in the above then I'd also recommend anything from
Siren whose games are less story but heavily focus on Insect and has similar gameplay mechanic to A house in the rift and Heros Harem Guild (i.e improve relationship for more content)
these are a few that I can think of off the top of my head but there is probably more so I'll come back and add a few later today/tomorrow