Is it permissible to wear two of the same garment in a public domain on Shabbat, such as two Kippot or hats one on top of the other?
This question occasionally arises when a person had forgotten his jacket in the synagogue the previous week, and now wishes to bring it home by wearing it over the jacket he wore to the synagogue. Similarly, this issue is relevant in areas with limited outdoor lighting, where people walking in the streets wear reflective belts over their coats. The question in such cases becomes whether we consider the individual as simply wearing an extra garment, which is, of course, permissible, or as carrying the additional garment. Since the garment is not "worn" in the conventional sense, this would perhaps constitute carrying through a public domain, which is forbidden on Shabbat.
This issue is subject to a debate between the Shulhan Aruch and the Rama (Rabbi Moshe Isserles, author of glosses to the Shulhan Aruch, Poland, 1525-1572), in Siman 301:36. The Shulhan Aruch rules leniently, allowing one to wear additional garments in a public domain on Shabbat, whereas the Rama rules that this is forbidden. Hence, for Sepharadim it would be permissible to walk in a public domain on Shabbat with two of the same garment, such as two Kippot, hats, jackets or belts, while for Ashkenazim this would be forbidden (Menuhat Ahav, Helek 3, page 323.)
Summary: It is permissible for Sepharadim to wear two of the same garment in a public domain on Shabbat – such as two hats or two jackets – while for Ashkenazim this is forbidden.