Is it mutar to wear an extra raincoat in rishus harabim in order to bring one over to a friend?
The question of wearing two items of clothing for bringing one to a fried is a matter of dispute between Shulchan Aruch and Rema. According to Shulchan Aruch, it is permitted. Rema, however, rules that the practice is only permitted when it is the normal way (at least at some time during the year) to wear two layers, such as two pairs of socks, or a jacket under a coat. For clothing that is never ‘doubled’ Rema rules that one may not wear two layers, and this is the halachic ruling for Ashkenazim. If there are people who wear two coats, one thinner “undercoat” and one thicker overcoat, the practice would be permitted even when the intention is to bring one of them for a friend. However, because as far as I know the general practice is not to wear two coats, it would not be permitted to do so.
Sources: Shulchan Aruch and Rema, OC 301:31; see Eliyahu Rabba (301:64), who writes that the prohibition is only rabbinic.