Alternatives to independent verbs for encoding desiderative meaning

Quite a few languages have desiderative as an affix within the verbal system (whether it is analysed as an affix or a full mood being irrelevant here). Japanese and Sanskrit do, for example. It is fairly common (as one would expect) for agglutinating or polysynthetic languages to have one such as Quechua, Finno-Ugric or Turkic languages. It is by no mean universal for these languages: while Hungarian has such a suffix Finnish (and I believe Estonian) lacks it.

Desiderative construction otherwise tend (again not unexpectedly) to be mediated via an auxiliary verb (in Nahuatl, that verb is one of a couple that can be directly integrated into other verbs).

Note that desiderative applies (typically) only to the subject. That is, a form like "I want X to Y" is not a desiderative per se. More accurately, in most language with derivational desiderative affixes, these affixes do not have a "separate" argument structure the way an auxiliary verb an have, so they cannot insert an additional argument. Indeed in Nahuatl, that is exactly what you'll see:

Ticchīhuaznequi (You want to do it)

Ticnequi nicchīhuaz (You want me to do it)

I have not found an easy way to search for information about the three-argument version ("I want X to Y") cross-linguistically, but I'd wager it tends to be formed with some form of Optative or Subjunctive structure.