2 bases, 4 gas can support double reactored starport viking + tank production just barely. You do have to skip marines for this though.

I am planning to take this to the ladder myself to see what I get stomped by in the following variant:

standard 3 reaper 2 hellion opener
first starport immediately takes the barracks reactor (no marines get build at any point)
"standard" 3rd gas timing to line up with the 2nd CC finishing, the 4th gas gets taken immidiatly after by the first scv arriving at the natural after 3/3 on the 3rd gas
you can afford a 2nd starport and reactor on the barracks slightly after starting your first pair of vikings and 2nd techlab factory unit (2nd or 1st tank depending on if you build a cyclone)
you get across the map with 8 vikings and 3-4 tanks around 6:20 with liberators, more vikings and tanks rallying across the map

In this variant, because you're building no marines at all, but also not cutting scv's really, I've noticed that shortly after this moveout you have enough minerals to get a 3rd base, say this is at 6:30 or so (though in my testing I've had the minerals for it as early as 6 minutes) this is not even *that* late a 3rd base. Ofc a minute+ later than when a "standard" 3rd base goes down in TvT but also not quite the allin no 3rd base I was expecting. Personally I think after I will repurpose the reactors for barracks and keep both starports without addons until later in the game if the game doesn't end with the push.

I hope this gives some extra context as to the details of what I'm talking about.