(ii) Divine Simplicity: God is absolutely simple.
(iii) God-only World: A world where only God exists is possible, but not necessary.
This isn't a genuine aporia, but it's interesting to think about anyway. (i) is the premise that every truth has a truthmaker, and some of us who find truthmaker theory attractive find it attractive too, (ii) has good arguments supporting it, and (iii) is an entailment of most Abrahamic religions.
If (i) and (ii) hold, by most truthmaker principles (iii) doesn't hold; if (i) and (iii) hold, God must sometimes differ between worlds and (ii) doesn't hold; if (ii) and (iii) hold, it can be true that only God exists without a corresponding truthmaker in the God-only world and (i) doesn't hold.
Is there a way out by rejecting the underlying principle that truthmakers necessitate their truths? Here is an argument from Armstrong (by reductio) that we shouldn't do this:
Suppose that a suggested truthmaker T for a certain truth p fails to necessitate that truth. There will then be at least the possibility that T should exist and yet the proposition p not be true. This strongly suggests that there ought to be some further condition that must be satisfied in order for p to be true. This condition must either be the existence of a further entity, U, or a further truth, q. In the first of these cases, T + U would appear to be the true and necessitating truthmaker for p. (If U does not necessitate, then the same question raised about T can be raised again about U.) In the second case, q either has a truthmaker, V, or it does not. Given that q has a truthmaker, then the T + U case is reproduced. Suppose q lacks a truthmaker, then there are truths without truthmakers. The truth q will 'hang' ontologically in the same sort of way that Ryle left dispositional truths hanging (Ryle, 1949). (Truth and Truthmakers, pp. 6–7)
Most correspondence and truthmaker theories are going to demand a principle at least as strong as truthmaker necessitarianism.
What about negative "entities", like absences and limits? Then we have our truthmakers and can safely claim that God is the only existent in the God-only world, but I doubt this is in the spirit of what most Abrahamic religions want to affirm by (iii).
Theists' best bet is to reject (i)—truthmaker maximalism. But is it really okay for those who find truthmaker theory convincing to just give up on it as soon as the going gets tough?