about 22 families in BugGuide's area containing a total of a few hundred species
The uropods set at the tip of the telson (vs at or near the base of the telson) is highly distinctive for this suborder. The only other suborder in North America with the uropods set like this is Microcerberidea, which are represented by the extremely bizarre Microcerberids in Bugguide's range.
There are 4 superfamilies (Aselloidea, Gnathostenetroidoidea, Stenetrioidea and Janiroidea) which are told apart by the pleopod arrangement. Ecology also helps, the Aselloideans are the only freshwater representatives of Asellota in North America (and all but 2 small-ranged cave species are in Asellidae), while the other three are marine. Gnathostenetroidoidea and Stenetrioidea each only have one family in North America (Gnathostenetroididae and Stenetriidae respectively), while Janiroidea has about 18 families off of North America.
Key to superfamilies in North America
1a. Pleopod 3 operculate, with shorter pleopod(s) visible in front of it → 2
1b. Pleopod 3 not operculate, either pleopod 1 (♂️), pleopod 2 or a combination of the two acting as an operculum, the resulting operculum with no shorter pleopods in front of it → 3
2a. ♂️ pleopod 1 protopods separated; ♂️ pleopod 2 exopods large, circular, often fringed with setae; ♀️ pleopod 2 separated; mainland freshwater, ranging between southern Canada to south Florida, sometimes swept to sea after storm → Aselloidea (Asellidae and Stenasellidae)
2b. ♂️ pleopod 1 protopods fused; ♂️ pleopod 2 exopods small; ♀️ pleopod 2 fused; tropical-marine → Stenetrioidea (Stenetriidae)
3a. ♂️ pleopod 1 broad, opercular, with protopod present, rami separate; ♂️ pleopod 2 small and hidden behind pleopod 1; ♀️ pleopod 2 with protopod present; tropical → Gnathostenetroidoidea (Gnathostenetriidae)
3b. ♂️ pleopod 1 narrow, protopod fused to rami; ♂️ pleopod 2 large, forming operculum with pleopod 1; ♀️ pleopod 2 lacking protopod; widespread from the Arctic to tropical waters → Janiroidea (about 18 families)