Comment 19 by JoxerTheMighty :

If you don't mind explaining, isn't the Multiverse(which many accept as plausible) the hypothesis that there are indeed "knobs", and that each twist of each knob produces another universe/reality, according to our model? How come the multiverse then isn't considered a fallacy?

The multiverse hypothesis was not primarily considered as a solution to the fine tuning problem, the existence of many universes follows form certain theories about the nature and the beginning of our universe, its a consequence of certain aspects of quantum field theory. And the footing of this hypothesis is rather poor compared to the attention it gets. I think the best answer to the question why the fundamental constants are the way they are is "We don't know. Yet."

I wouldn't advice any theist younger than 70 to write a book based on the fine tuning argument, because there is a large chance he will live to see at least part of it come apart, when we start understanding it.