I fear this one is another of my "longshot" questions, in that I can only recall a few bits of the story.
A married couple, whom I believe are of Hispanic/Latino ethnicity, decide to give cloning a try. There is a service in the story that allows you to be cloned on a temporary basis, and can tweak/customize your clone. The original body is kept safe in a tank or some sort of stasis (I can't recall).
The story POV treats the clones as if they are the original person. There may be an element of transferring the consciousness of the original body into the temporary clone. I cannot remember on that point.
In any case, the couple in the story give it a try. There may or may not be multiple cloning sessions for them. The only one I can recall for certain is that the husband and wife agree to try becoming the opposite gender.
The most vivid and easily recalled part of that experiment comes when the husband and wife become intimate that evening. I recall the husband (now a woman) asking his wife how she deals with having breasts, and that he feels very awkward about them and how he's supposed to carry himself. Something like that.
I'm pretty sure, though not 100% positive, I read this one in an anthology. If I had to guess at a timeframe for publication, I'd say the 1970s would seem a likely era. I don't think its much older than that, given the subject matter.