Well, I just got here... and I've read all the posts and this is really a fun one.
There is a score, I saw it when I was in High School, by Henry Cowell that did use 12th notes and 7th notes, and all kinds of other things like that (memory is a little dull on this point after 40 some years). Cowell used the note heads that we call 'shaped notes' that were (are) used in some church hymn books (they use them to denote a kind of solfeggio system, Cowell was using them as a rhythmic notation).
The idea, as best I understood it at the time, was to take the duration of say, a 12th note (and yes, it IS one third of an eight note triplet) use it as a single note. So then you might have something like quarter note, 12th note, quarter note, 12th note, 2 eighth notes, and a 12th note. Now, it takes NO imagination at all to realize that this is, 1.) Insanely difficult to read and 2.) really nothing more than a way of notating a rubato tempo, or 3.) a composer wanting to have the feel of improvized music, but unwilling to give up control of the music.
Given an ensemble of musicians that could deal with this sort of thing, I suppose a composer could create a music that had a clearly notated way of controlling mixed rubato... I leave you all to ponder the musical value of such a thing.
Alot of Charles Ives' music was composed with multi-tempos in mind... and really there is not a clear way to notate that within our current system. Ives did the best he could with a wild mix of nested sub-divisions.
In the end, we may find that it's best for composers to set up a musical situation and let the performers react to that, rather than control everything from the written page.