“Post Format” is simply a custom taxonomy, and it is – by design – not extensible.
I would recommend just implementing this procedurally, by only using specific tags with specific Post Formats.
EDIT
I would start with the Codex entry on Post Formats.
Here’s a little primer I wrote on using Post Formats as a taxonomy.
As for tutorials for implementing Post Formats, there are several. Just try a Google search for “WordPress Post Formats”.