I think most of the ones on DS are what you are looking for.
Also there's the Zero Escape games. Also story-heavy hybrid VNs with adventure+puzzle solving elements, and multiple endings.
Thanks guys, playing the first Danganronpa on a psp emu, good shit.
Sure, don't know if you're aware but there are PC (Steam) ports for the Danganronpa games. Might make your life easier compared to fucking with emulators.
I know, but the psp version was lighter and I'm on a slow connection so I just downloaded that, so far the emulator works fine.