Star Fox (SNES), Star Fox 2 (SNES mini), Star Fox 64, Star Fox 64 3D, Star Fox Zero and Star Fox (Switch 2), while having minor gameplay differences, are all retellings of the same in-game story (the eponymous Lylat Wars).
Moreover, Star Fox was kind of... programmed by teenagers. Miyamoto is credited as both the producer and designer, but both Cuthbert and Goddard were 18 or 19, and Wombell (artist and designer) was maybe in his mid-20s.
Star Fox's development is an incredibly wild story where British teenagers argued what the SNES could do with bespoke hardware, and they ended up being shipped out to produce it because Nintendo felt they couldn't ever do it themselves. It all started with Argonaut's demo of what would eventually be released in Japan as "X". Entirely software-based 3D, on the original Game Boy.
There's actually a very humble quote by Miyamoto where he learned that someone can't just get better as a function of age and experience, after he clearly realized that these teenagers could produce something no one else in Nintendo ever had a hope of. Perhaps it's why the franchise has done so little -- Nintendo's just not in a remotely similar headspace the Argonaut lads were.
The previously unreleased Starfox 2 is not a retelling, it is a proper story sequel. That is the one game where you're wrong, every single other game is a remake, with Starfox Zero the most tenuous one, but still a reimagining. They've remade the same story five times.
Between 1 and 2 was the 3DS remake which added levels and cleaned up the story some. The Switch Starfox includes those parts, too, from what I've heard.
A remake (1) of a remake (2) of a remake (3)
(1) A remake (Switch 2 Starfox, a remake of StarFox 64)
(2) StarFox 64 (A remake of Super Nintendo's StarFox)
(3) ??? I don't know what the 3rd level of remake you mention is, but I'm curious!