Compression technique exploiting common similarities
Of course it is possible.
For example, you could define the trailer of a movie as the sequence of movie sequences it shows plus the trailer-specific overhead it uses. If the movie itself is at hand when you want to watch the trailer, then everything goes well.

Yet in general...either you would have to add tons of metadata to each file (e.g. "contains sequences in which blue-eyed guy fiddles around with a knife"), thus increasing all files significantly, or you would have to run some pattern-matching algorithms over all your movie database. And your file will be very context-dependent, i.e. if one of the files you rely on changes, then all hell breaks loose. That does not sound practical to me.

Note that most lossless compression techniques also share patterns that appear across different files. So if you gzip a set of very similar mp3s, then some notable compression should happen.