Q. Does one fulfill a mitzvah (of Biur Chametz) with every kezayis of chametz that is burned on erev Pesach?
A. Mishna Berura (445: 10) writes that one should not sell or give away all his chometz by Erev Pesach to a Gentile. He should rather reserve at least a kezais – olive volume of chometz, so he can comply with the mitzva of Tashbisu or destroying the chometz, even according to Rav Yehuda who opines it should be burned.
However, in principle since we follow the opinion of the Sages, that the mitzva is not having chometz, he has fulfilled already that mitzva. (See Minchas Chinuch 9, who maintains that Rishonim also disagree on this).
Some compare it to the mitzva of Tzitzis (Chelkas Yoev O.H. 9, Mekor Chaim 431, et.al.) and one may argue that it may be similar to wearing more taalesim, that is tantamount to more mitzvos. However, others compare it to the mitzva of shechita, in which case we don’t have to search for animals to sacrifice. (Divrei Chaim 1: 9, Avnei Nezer O.H. 318, et. al.).
Horav Shlomo Miller Shlit’a would likely point out, that the common minhag is not to look for more than one has, as is the Mishna Berura’s opinion.
Rabbi A. Bartfeld as advised by Rabbonim of the Kolel of Toronto Halacha Group