Adding a deity to the explanation requires adding an "entity" completely nonexistent in the current models that are the basis for the multiverse, i.e. those within quantum theory and cosmology.
The root of my question is I am uninformed of anything with quantum theory or cosmology that makes a multiverse more likely than deism. Do you have specific examples from quantum theory or cosmology that makes a multiverse more likely?
I think the deist can insist "My explanation is the most parsimonous. I have just the one thing, a deity. You have a kludge of a dozen different forces and laws and variables."
The "parsimony", the "simplicity", the unit in which we count entities - is that of Kolmogorov complexity. "A dozen different forces and laws and variables" is significantly simpler, Kolmogorov-wise, than a thinking entity. There is orders of magnitude less things to specify about the former than about the latter for a complete description.