In general, the rule limiting the number of letters in a partial phrase applies to everything -- titles, quotations, everyday speech, geographic locations, etc. In fact, I would think one should be especially careful about using partials with titles and quotations, simply because if the title or quotation isn't that well known, it could frustrate a lot of solvers as being poor or obscure fill. As for the permitted number, that changes depending on the publication. It's 5 for the New York Times on each day, but the LA Times allows 6 letters on Sunday puzzles.
Having said that, the rules of constructing can be bent if it serves a good purpose. I think it is theoretically possible that a theme of the type that you're proposing could work, though it might be tricky. SJS notes that SO YOU THINK would not work for the original clue you've chosen because the word "you" appears in both the clue and the answer. But, it may be possible for you to build a puzzle in which the theme entries are each clued as partial phrases, provided that each of those phrases share something in common and can be reasonably intuited.
For example, maybe the theme answers could each be sections of well-known movie titles, or TV titles, or song titles, but at the same time they function as common, everyday phrases that could stand on their own without needing to be clued as partials (but you clue them as partials anyway because that's part of the puzzle's gimmick). The trick, then, would be to find the titles that could serve that purpose. It may also help to find a movie title/TV title/song title that gives the puzzle a good reason why the theme answers are clued as partials, and then use that as a final theme entry. Maybe the TV show LOST could work as a unifier for that kind of theme, by cluing it as "TV show set on an island ... or what the answers to x-, x-, x-, and x-Across are compared to their clues."
These are just ideas I'm brainstorming, and they shouldn't necessarily be taken as sage advice. It's just how I would go about picking theme entries and trying to get a theme like this to make sense to a solver.