'Deepen' after "git clone --depth=1"?

Suppose I want to make a shallow clone of a repository for some size-sensitive application. I may later want to fill out the complete history of that repository, so that I can work with it as if I had done a full-depth clone to begin with. Is there an existing porcelain command/option to produce that effect? If not, is there a fundamental reason why this couldn't be implemented? It looks like this is something fetch-pack should be able to do, but its documentation doesn't seem to describe how. Also, the man page for fetch appears to lie, in that --depth=n (where n is greater than the clone depth) doesn't have any noticeable effect.

If the answer is simply "no one's written the code to do it yet", I'll be happy to provide the necessary round tuits.

Phil