Adolf desires that more desires be thwarted than fulfilled. [A 'desire that P' is 'fulfilled' if P is in fact true, 'thwarted' if P is false.] Further suppose that - apart from this desire of Adolf's - there are in total an equal number of fulfilled and thwarted desires in the world. It follows that Adolf's desire is fulfilled if and only if it is not fulfilled.
The problem with Adolf is that he was put in a context where his desire became self-referentially paradoxical. This situation could potentially arise whenever you have a desire that refers to 'all desires'. But it's logically impossible that a desire could have its own thwarting as a fulfillment condition - that's equivalent to a statement having its own falsity as its truth condition! So I think we must hold all such desires to be impossible. (It would seem odd to say they are possible some times but not others, depending on the external context. Why should the existence of an internal desire depend on the external world?)
Patrick suggested to me that the analogous liar sentence is not always impossible. Imagine a sheet of paper headed with the sentence: "Most statements on this page are false." But suppose the rest of the page contains an equal number of true and false statements. The original statement would now be true iff it is false. In other words, the context converts it into the liar sentence. Contradictions are impossible. Since it's impossible to have a statement truly asserting a contradiction, we must conclude that the apparent sentence is in fact meaningless (it refers to no proposition) in this context.
But we do not want to say the original sentence is always meaningless - that would seem clearly mistaken. For example, we can imagine the rest of the page is instead filled with false statements, in which case the original statement will be plainly true. It is not plausible to claim the statement is meaningless in such a harmless context. It is not really a liar sentence. It is merely a potential liar sentence. Whether the paradox is realised or not depends on the context.
This suggests that Adolf's desire should similarly be possible in appropriate contexts. It is unproblematic to desire that more desires be thwarted than fulfilled, so long as the sum of other desires is not exactly balanced between the two.
As I noted before, it does seem odd to say a desire is possible in some contexts but not others. But given the quasi-indexical nature of this desire, its context-dependence is perhaps not so surprising after all. In a sense, the meaning of "most statements on this page are false" will vary depending on which page it refers to. Similarly, the content of a desire that "most desires be thwarted" will depend on the background set of all desires that it refers to. In most contexts, the desire will be unproblematic (contrary to my earlier suggestion). Only in a few specific contexts will a paradox arise. So whether such desires are possible will depend on their external context.
Hopefully that doesn't sound too ad hoc. I guess an alternative solution to the liar paradoxes would simply be to accept true contradictions and adopt a paraconsistent logic, but I'm a little reluctant to do that.