There is a way that an Anselmian could attempt to prove any number of interesting (and not always welcome) conclusions to other Anselmians by distinguishing between a greatest possible being and a perfect being. Typically, these terms seem to be used as synonyms, but it is interesting to see what happens when we consider how they might differ.
First, consider the fact that people disagree about the modal status of some things (e.g. is libertarian freedom possible, is God a necessary being, etc.) There seem to be a variety of conceivable worlds with different necessary truths. One can conceive of a world where God is a contingent being, and likewise one can conceive of a world where God is a necessary being. Call these worlds that vary in their necessary states of affairs “epistemically possible worlds” (EPWs). Obviously, since they vary in their necessary states of affairs, only one at most is metaphysically possible. But more than one EPW is epistemically possible.
Now it seems that different EPWs may have different greatest possible beings. There may be one EPW where less power is available to be had than another EPW, so a conceivable greatest possible being would be less powerful in the former EPW than in the latter. Or maybe in EPW(1) it is possible to know future contingents but it’s not in EPW(2). Thus a greatest possible being in EPW(1) knows future contingents but a greatest possible being in EPW(2) does not. Granted, either EPW(1) is metaphysically possible or EPW(2) is; they are not both metaphysically possible. But they are both epistemically possible.
Now here’s the crucial suggestion: If greatest possible beings vary in their natures from one EPW to the next, then one could suppose that not all conceivable greatest possible beings are perfect beings. Suppose a perfect being would know future contingents. Then if EPW(2) represents the actual set of necessary states of affairs, then while there may still be a greatest possible being, there is not a perfect being. (Another way to put this is that even if one grants that there is a greatest possible being, it may yet be true that perfection is not possible).
Like I said above, one could use this distinction to prove all sorts of things. Consider this argument:
1. A perfect being is metaphysically possible.
2. If EPW(3) obtains, then a perfect being is not metaphysically possible.
3. Therefore , EPW(3) does not obtain.
4. Any EPW(n) is metaphysically necessary if it obtains (is actual) and metaphysically impossible if it does not obtain.
5. Therefore, EPW(3) is metaphysically impossible.
The premises are (1), (2), and (4). Premise (1) is an axiom accepted by all relevant parties. (4) is a result of the principle that propositions about necessary states of affairs are either necessary or impossible; they cannot be contingently true. (2) is the premise that the arguer needs to defend. So let me give some content to EPW(3) and defend premise (2).
Many Anselmians would maintain that libertarian freedom exists. Suppose EPW(3) includes the proposition “libertarian free will is possible.” One may fill out the rest of the content of EPW(3) with whatever seems plausible, so long as it is consistent with EPW(3)’s including that proposition. Now in EPW(3), where libertarian free will is possible, God cannot actualize any possible world. For example, God cannot necessarily actualize a world where free creatures always choose to do good instead of evil (or even if he could [weakly] actualize such a world, there will still be others that he cannot). He is not in control of what people freely do, so (to borrow some molinist terminology) there are some possible worlds that are infeasible for him to actualize. But suppose that in another EPW, namely EPW(4), where libertarian free will (and other sorts of indeterministic contingency) are impossible, God is able to actualize any possible world. He has specific control over every possible event or action that could take place. I will use the following (rough) definitions:
A being G is maximally sovereign =def G can actualize any possible world except those worlds which are not feasible for him to actualize.
A being G is perfectly sovereign =def G can actualize any possible world.
(For simplicity’s sake, I have ignored temporal considerations related to world-actualization). In EPW(3) God is as sovereign as a being can possibly be (he is maximally sovereign), and therefore, given what we know, he is at least in the running to be EPW(3)’s greatest possible being. But in EPW(4) he is not only as sovereign as possible in that EPW, he is also perfectly sovereign (as per my definition). Now suppose an Anselmian argues that, intuitively, a perfect being would be not merely maximally sovereign, but also perfectly sovereign (I don’t mean to stack the deck in his favor by using the term “perfectly sovereign”; I just couldn’t think of any better term). There does seem to be some intuitive force behind this idea. If that intuitive force is strong enough, then premise (3) will be granted, and the Anselmian will be forced to abandon libertarian free will (as well as other sorts of indeterminacy).
Now for my own part I have leanings towards both Anselmianism and libertarian freedom. I have some under-formulated thoughts on how an advocate of both might reply to this argument, but for now I will save those ideas for another day (when I have had more time to think them through, perhaps) and just leave this as food for thought. Also, it is worth noting that if this argument proves untenable, it will matter a great deal whether it fails because the general strategy employed is defective, or because of something peculiar to this case where it is employed against libertarian free will. If the latter, then other arguments of this form, used for or against other disputed divine properties, may still be successful. But if the former, then no such argument will succeed.