If you call it a "house with a septic tank", things are pretty standardized about how it should be treated. It has to be correctly sized for the number of people in the house, the leach field has to be a certain size depending on the results of a percolation test, etc. I can imagine there is fairly little wiggle room.
If you call it a "farm operation with an anaerobic digester" that recovers
energy to use for some farm operation, say drying grain or heating a barn, then you probably have a lot of wiggle room. You deal with a different group of people who are less interested in following a prescriptive checklist and more interested that you have the proper engineering to back it up. Instead of the county health department, you probably deal with the state Department of Environment and Natural Resources and they will want to make sure you are not fouling the air or the waters.
I guess it's going to depend on the county you are in and your zoning. The more agricultural it is, the easier you can call it a biodigester. In all my reading, I have never seen rules about what you can't toss into a biodigester. Could be
chicken manure, pig manure, spoiled silage, biomass, even what's pumped from household septic tanks.
What you describe almost sounds like the biodigesters that are popular in Vietnam: