In recent years, several philosophers of religion have offered reasons for thinking that if theism is true, the actual world probably comprises many universes. These philosophers argue that theism, plausibly, entails the existence of a multiverse, often referred to as the theistic multiverse.
One might ask whether this development negatively impacts the credibility of the fine tuning argument for theism. Do arguments for the claim that theism entails a theistic multiverse, if successful, render the fine tuning argument untenable? I think that this is not the case. Those arguments do not prevent us from running a successful fine tuning argument. For we can run that argument as follows. Given the scientific datum of the fine tuning of our universe there are precisely four options to choose from:
(1) The fine tuning is due to mere change,
(2) The fine tuning is metaphysically necessary,
(3) The fine tuning is explained by there being a naturalistic multiverse [*],
(4) The fine tuning is explained by the supernatural design of either a uni- or a multiverse.
Against (1) and (2) the familiar objections can be raised, and against (3) one could raise all known objections against there being a naturalistic multiverse, such as Penrose's objection mentioned in his book The Road to Reality from 2004. After all, in the case of (3) we are talking about a naturalistic multiverse, which is precisely the kind of multiverse these known objections are aimed at. This leaves us with (4), which is precisely the conclusion of the original fine tuning argument. Given (4), the supernatural designer might have created either a single universe or a multiverse (being in that case of course a theistic, not a naturalistic, multiverse). The answer to the question which of both scenario's the designer has brought about can be left open, or, one could try to argue for one of both scenarios. But this does not change the main conclusion as established by the fine tuning argument, namely the existence of a supernatural designer, who brought about either a single universe or an entire multiverse.
[*] A universe is a causally closed aggregate of space-time and all of its contents. A naturalistic multiverse is a possible world that contains two or more universes and nothing else.