There are a variety of different issues here. It seems that you are talking about some sort of notion of multiverse that is somewhere between Tegmark II (different physical constants) and Tegmark IV (different laws which could be anything consistent). Note that it is not in general easy to define what one means by the number of laws being finite or infinite. To use an analogy to a common axiomatic system, ZFC technically has infinitely many axioms, but the axioms are so regular that one might as well regard them for intuitive purposes as a finite set of rules (since we have a short set of rules about how to state the axioms). So what does it mean for a system to have infinitely many rules? Does it mean that there’s no finitistic specification in some sense? Maybe the total set of rules can’t be enumerated by a Turing-computable process? If so, we don’t a priori know that our universe has a finite number of rules. Moreover, how does one handle in this framework constants that aren’t Turing computable? Conceivably all the laws for our universe are a finite set except for say the exact value of the fine structure constant but there’s no Turing machine which given input n will output the nth digit of the fine structure constant. Does our universe then have a finite or infinite number of rules?
There are a variety of different issues here. It seems that you are talking about some sort of notion of multiverse that is somewhere between Tegmark II (different physical constants) and Tegmark IV (different laws which could be anything consistent). Note that it is not in general easy to define what one means by the number of laws being finite or infinite. To use an analogy to a common axiomatic system, ZFC technically has infinitely many axioms, but the axioms are so regular that one might as well regard them for intuitive purposes as a finite set of rules (since we have a short set of rules about how to state the axioms). So what does it mean for a system to have infinitely many rules? Does it mean that there’s no finitistic specification in some sense? Maybe the total set of rules can’t be enumerated by a Turing-computable process? If so, we don’t a priori know that our universe has a finite number of rules. Moreover, how does one handle in this framework constants that aren’t Turing computable? Conceivably all the laws for our universe are a finite set except for say the exact value of the fine structure constant but there’s no Turing machine which given input n will output the nth digit of the fine structure constant. Does our universe then have a finite or infinite number of rules?