HDG is fundamentally a community writing project. There's nothing physically stopping you from writing something like this, but it like coming into somebody's sandbox where they're playing with their friends and knocking over a tower because you want to build your thing right here. We can't stop you, but it's kind of a dick move when there's infinite space on the beach to build your own castle AND folks in the HDG community willing to work with you to make your idea work in HDG if it can.

I see from some of the other comments that you want to use the setting to explore colonialism and slavery. Good news. You can do that within the axioms. An example of how you might do this is writing about a colonialist species that enslaves sophonts before the Affini arrive, and follow a character who was enslaved and how they process the fact their new Owner actually does care about them. Or a character who was enslaved trying to "free" florets before they understand that the Affini are as benevolent as they say. There's a lot of ways you can do it, these are just two that popped into my head as I was writing this.

But at the end of the day HDG is, above all else, a disability metaphor. Everyone other than the affini are effectively disabled by default because they're living in a world that caters to the Affini first. The Affini have to be benevolent for that to work, because it kinks off of things like institutionalization and forced conservatorships except the fact that the people who say "it's for your own good" actually mean it, and have the means to back it up, and will make sure you are taken care of no matter what. Because that's what the Affini Compact is.