Brian Leftow has defended a version of the cosmological argument which posits that if God possibly causes abstract objects to exist, and abstract objects exist necessarily, then God must exist necessarily. One reason Leftow puts the argument this way (presumably) is to avoid the problem of compromising God's unique aseity. If God is not the only self-existent entity, then that is apparently a difficulty.
I wouldn't go that far. In fact, even if the Platonists are correct in saying that abstract objects have necessary existence, God's unique aseity may be salvaged by pointing out that only God stands in a causal relationship to other entities. Abstract objects, if they exist at all, are causally inert, so their aseity is of one type, whereas God's aseity is of another type. Nevertheless, the idea of anything other than God existing a se does leave the Christian, myself included, with an uneasy feeling.
The problem I see with Leftow's argument is that it doesn't seem to be possible to cause abstract objects, for the reason given above. If abstract objects literally cannot cause anything, why think they can be caused themselves? St. Augustine, having been trained in the neo-Plantonic tradition, solved this difficulty by postulating that abstract objects exist as concepts in the mind of God. This means that even though abstract objects exist a se, and are not caused to exist, they are still dependent on God's mental activity (theological conceptualism). I think we may incorporate Leftow's modal argument with this conceptualist model of abstract objects:
1. Abstract objects are possibly necessary. (Premise)
2. Whatever is possibly necessary is necessary. (Premise, S5)
3. Abstract objects possibly exist necessarily as mental concepts. (Premise)
4. Therefore, abstract objects are necessary concepts of a mind. (From 1, 2, and 3)
5. Abstract objects cannot be concepts only in contingent minds. (Premise)
6. Therefore, abstract objects are concepts of a necessary mind. (From 4 and 5)
Briefly, in support of (5), abstract objects (if they exist necessarily) cannot be concepts of just any mind. For, there are possible worlds in which contingent minds (such as you and I) do not exist, and so abstract objects must be concepts of a necessary mind in those possible worlds. Given (2), it follows that a necessary mind also exists necessarily.
Of course, there are also positive reasons (other than S5) to conclude that abstract objects must be mental concepts. One of these reasons is the causal objection against Plantonism.