Personally I doubt it. I expect it to get the Mario Kart/Smash treatment with just one per console
The thing is though that Splatoon 2 seems more like Splatoon 1.5 in a lot of ways. Just a lot of tweaks and polishing to the original game, not a lot of big changes, since I'm sure they wanted to get a Splatoon game out on Switch asap. So I wouldn't be surprised to see Splatoon 3 in a couple years that is more of the true evolution of the franchise.
I'd say they wanted it out asap to avoid any hole in the lineup for this year to avoid the infamous Wii U droughts on the Switch. Splatoon 2 was easy because not too much had to be changed on a technical standpoint from the original game, being able to retain most assets, just maybe polishing them up a bit. Otherwise there wouldn't have been any big game release between Arms and Fire Emblem Warriors/Pokkén tournament late september (don't think they knew a release date yet for Mario & rabbits at that point), so a very dry summer for the Switch.
Splatoon 3 will come, but I doubt it will come this decade