The interaction between differentials on a graded ring and chain-homotopy equivalences

I am wondering about the following question:

Given a differential graded algebra $$A$$, how many other differentials can we put on the underlying graded ring of $$A$$, which are also chain-homotopy equivalent to $$A$$ ?

I'd like some references, perhaps, that may address the above question. Or if anyone here knows about results related to this question, please cite them here.

Thanks!