"extension of" or "extension to"?

Solution 1:

As so often in English, both of these are acceptable, and mean more or less the same thing.

If you want to be super-precise you might argue that the first example (extensions to...) means that you are describing something that is related to the basic model and yet differs enough to be distinct; whereas the second example (extensions of...) concerns something that goes beyond the basic model but still remains essentially part of it.

If you want alternative phrasing, you might say "we describe some ways to extend the basic model" (for the first) or "we describe some ways to apply the basic model" (for the second). Without further context it's hard to say which is better.