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1) OFFERING TWO LIMBS AT A TIME FROM A FORBIDDEN MIXTURE
OPINIONS: The Mishnah quotes Rebbi Eliezer who rules that in a case in which the limbs of valid Korbanos became mixed with the limbs of a blemished animal, if one of the heads was offered already, then the rest of the heads may be offered. In the Gemara, Rebbi Elazar states that Rebbi Eliezer permits offering the remaining, similar limbs only by offering two at a time, but not one at a time. RASHI (DH Ela Shenayim) explains the reasoning behind this. When two limbs are offered at the same time, one of them definitely is a permitted limb from a valid Korban. Since ("Migu") one of them definitely is permitted, one may assume that the second one is also permitted and that the forbidden limb was the first one that was offered earlier.
Does this reasoning apply in a case in which the limbs of valid Korbanos became mixed with the limbs of two blemished animals? In such a case, it does not suffice to offer two similar limbs at a time, because it is possible that both limbs are from the blemished animals! Will it suffice to offer three limbs at one time, or must one offer four limbs at one time (in order to ensure that an equal amount of permitted limbs are sacrificed together with the invalid ones)?
(a) The SHACH (YD 110:47) asserts that four limbs must be offered at one time. As Rashi explains, when there is only one prohibited item in the mixture, one may offer two limbs at a time because the principle of "Migu" dictates that just as one limb is definitely permitted, the other is also permitted. However, when there are two prohibited items in the mixture, offering three limbs at a time does not suffice. Although it is true that one of the three is definitely permitted, the "Migu" that one is permitted proves only that one other piece is permitted, but not that two other pieces are permitted; since there were two prohibited items in the mixture, there is a chance that both of the other two are the prohibited items. In order to apply the "Migu," there must be two pieces of definite Heter, and only then does the "Migu" apply to determine that since two are definitely permitted, the other two are also permitted.
Accordingly, the Shach rules that when two pieces of Isur become mixed with pieces of Heter and one piece was offered already, Rebbi Eliezer maintains that in order to permit offering the remaining pieces, four pieces must be offered on the Mizbe'ach at one time.
(b) The CHAZON ISH (YD 37:20) disagrees with the Shach. He asserts that there is no such logic that "just as one limb is definitely permitted, the other is also permitted." The Gemara cannot mean that the reasoning of "Migu" permits offering the two pieces together. Rather, the reason why Rebbi Eliezer requires that two pieces be offered at one time is that the "collective" Korban being offered on the Mizbe'ach must have the title of a permitted Korban, a Korban of Heter. As long as there is definitely a piece of Heter being offered, the offering has the title and status of Heter, and it is not consequential that the other piece might be Asur. Accordingly, even if there are two other pieces that might be Asur, the fact that one piece is definitely one of Heter gives the Korban the status of a permitted Korban and the mixture may be offered on the Mizbe'ach. (Mordechai Zvi Dicker)