In a canon, a piece usually starts from one melody and expands into several. Is it possible to create sort of sub-canons within the piece? Say I came up with an idea in the middle of the piece that I briefly wanted to carry down to the other instruments. Is this doable or must it slowly disappear into the rest of the piece?
I was going to make this a comment for clarification, but I'll frame this as an answer since I don't yet have a 50 reputation...
At the risk of answering your question with a question... I will do exactly that: Is this for a composition? Or for a theory exercise?
For a theory exercise: Yes, since a canon is the broadest term for a piece with this repeating, round or fugue-like quality. Essentially, if you start all voices on the same melody (at different starting times) you have a canon... how you develop it is irrelevant.
For a composition: YES!! It's your music, write what you want! If you look at even Beethoven, he breaks every "rule" you can think of. Bach even breaks all the rules we learn (which mainly come from him). And we are 300+ years past that.