The argument for there being lots of universes with different physical constants is similar. However, there’s a big difference between physical constants and mathematical constants. In a nutshell there’s: 1) same universe, but far away, 2) quantum multiverses, 3) related universes with different constants, and 4) “other”. String theory and eternal inflation imply that new universes are constantly being formed with slightly different physical constants. Lee Smolin’s “Fecund Universe” theory, where every new universe is a black hole from a higher universe, implies that universes literally evolve to be better at producing black holes.