I wonder how hard it would be for mobile home manufactors to support the modular stacking of units. It would look redneck as hell, but could probably go up even faster then wooden prefabs that still needs a building finished around it
Would need some way to get up and down and toilet/water.
Tbh by the time you've done all that you might as well just build a normal modular high rise (that's how the local budget hotel did it, nearly whole thing turned up as a series of containers each prefitted with plumbing and power, then stacked together, hooked up and done, it went up insanely fast).