First of all, it should be extends, not extend.
Here is one variation:
Model A extends from stage C, which fits only one dependency relationship, to stage D, which estimates different dependency relationships.
But this actually says two things. It says that stage C fits a single dependency relationship and that stage D estimates multiple dependency relationships, none of are the same dependency relationship as in stage C.
If this combined meaning isn't intended for stage D, then only one of the following two should be said:
Model A extends from stage C, which fits one dependency relationship, to stage D, which estimates a different dependency relationship.
Model A extends from stage C, which fits only one dependency relationship, to stage D, which estimates multiple dependency relationships.
My only other comment is that it's slightly strange to have fits in the first part of the sentence but estimates in the second part. Typically, if using a comparison, one or the other word would be used in both parts of the sentence. You've mentioned that it's appropriate in your particular case—but it still sounds odd.
The essential part of the sentence seems to be this:
Model A extends from stage C to stage D.
The rest is just information that you've added about each stage. That information doesn't have to be of the same type in each case—but it's a bit awkward when it isn't.