On who is involved in one mitzva does not have to do another. This has farther ramifications than most people think. The reason is the Shulchan Aruch puts together the opinions that one does have to stop in order to do another mitzvah along with the opinion one does not have to stop.

It is an argument in Suka 25a. Rashi, Tosphot, and the Baal Hameor all hold the argument there is going according to the opinion one has to stop. But the halacha is like R. Jose HaGalili that one does not have to stop. See the Rif, and the Baal HaMeor in the back.