On Monday Nancy Friedman offered this awkward example to me:
“One of the things that you always want to be for, whether you’re a Democrat or a Republican, is that you want everyone who’s eligible to vote to vote.” – Steve Schmidt, McCain strategist in 2008 (link)
There’s nothing syntactically wrong with this sentence, but the repetition of to vote might give you a moment’s pause. Nevertheless, the first to vote is an ordinary infinitival complement of be eligible (They are eligible to vote), in a relative clause modifying everyone (Everyone who’s eligible to vote is coming), and the second to vote is an ordinary infinitival complement of want in combination with a direct object of that verb (We want everyone to vote), and to vote to vote is merely part of what you get when you put these pieces together in ordinary ways.
Repetitions like this one — repetitions I’ll call Toto examples (Totos for short), after to vote to vote and in recognition of the passing feeling of oddness that they can produce (“Toto, I’ve a feeling we’re not in Kansas anymore”) — are quite common, though a careful stylist might want to avoid some of them as distracting. But then there are syntactic constructions that specifically call for repetitions of constituents. And still other configurations that you’d expect to be acceptable — more Toto examples — that are nevertheless just ungrammatical (for some speakers).