SSP and Headmaster have a different tone than Eternum and HH. So, that makes life easier, because I have more data points. Lets see what I come up with:
This took longer than it should have, because I was interrupted by and had to pay attention to a needy pussy. Cat tax at end.
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: It's just a rambling feel good kinda story that doesn't really go anywhere.
A House in the Rift: Feels a lot like Harem Hotel, not anywhere near as much content.
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: One of the classic "good games", heartfelt story.
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: story is similar to Eternum in scope and feel, different genre though.
: Feels a bit like SSP, ok story.
Burned: I second this one.
Come Home: Feels a bit like HH, decent story.
: Has no business being in this list. Hilarious though.
: A long ever growing feel good story with good world building. Not a close analog in tone to any of the examples though.
: Fools a lot like HH. Not a lot of story, but it's not bad.
: this is kinda SSP lite. Not as good on any front. But good.
: A story driven feel good story. Pretty high quality.
: is similar to Eternum.
: is an incestuous blend of SSP and Eternum
: Feel good story, on par with Eternum or HH.
Little Green Hill: I don't know that I would recommend this one, but it's basically an unholy union of all four games you listed. I'd at least look at it.
: Kinda like a mix of headmaster and HH.
: straight up story, kinda like Eternum or Out of Touch,
: Feels a lot like HH.
Malignant: This is the other game by the author of Burned. Not quite as humorous, more in the vein of SSP. Not a direct parallel to anything, but worth looking at.
: Not a direct parallels to anything you listed, but a good story.
: HH but not.
: Post zombie-apocalyptic story. Not close to, but inspired by SSP in my mind. If you like this, the authors other two games are just as good.
: same author as Eternum. Also excellent.
: Story driven world with lots of lore. Not a good parallels to anything you listed, but good.
Pale Carnations: Feels like Headmaster to me. Different but good. Has a story, but its not story heavy.
: Not a fantastic game, but it has a decent story, and feels a lot like Eternum to me.
Power Vacuum: not a lot of story, but the writing and humor and graphics all tickle me. Feels a bit like HH as written by Chuck Lorre.
Radiant: SSP lite.
: SSP lite plus HH with few choices, and its story driven.
: Story heavy, more feel good than SSP.
: Rambling story with little plot, enjoyable and an early favorite of mine.
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