In the context of religious arguments, some say that the constants of the universe are improbably finely tuned for the existence of life and order. The constants refer to things like the gravitational constant, the strength of the atomic weak force, etcetera.

It is my understanding that the order part is key; most other possible constants wouldn't allow for an alternate form of life, for example, because everything would be so far apart as to never interact, or so close together as to never vary in its state.

Some will respond that there may be a multiverse of universes, with random universal constants, so that some improbable universes are bound to crop up.

To this, it is responded that inventing a multiverse to explain away apparently purposeful tuning of universal constants doesn't really work. It's an excuse.

Now, I know that MWI was NOT invented to explain away anything, that it was presented as a possible explanation for certain observations well in advance of this kind of argument.

But, here is my question. Does MWI limit itself to alternate universes with the same universal constants, or does it predict also the existence of universes with different universal constants?