(Mishnah - R. Shimon ben Yehudah citing R. Shimon): The goats of Rosh Chodesh atone for a Tahor person who ate Tamei Kodshim;

More than this - the goats of the Mo'adim atone for a Tahor who ate Tamei, and also for Tum'ah that had no Yedi'ah at the beginning, and not at the end;

More than this - [outer] goats of Yom Kipur atone for a Tahor who ate Tamei, and when there was no Yedi'ah at the beginning, and not at the end, and also Tum'ah that had no Yedi'ah at the beginning, but there is Yedi'ah at the end.

Rabanan asked, did R. Shimon say that they can be offered in place of each other? R. Shimon ben Yehudah said, yes.

Question (Rabanan): Indeed, the outer goat of Yom Kipur may be used on Rosh Chodesh [since it was designated to atone for more]. However, how can a goat designated for Rosh Chodesh be used on Yom Kipur, to bring a Kaparah for which it was not designated!

Answer (R. Shimon ben Yehudah): They all atone for Tum'ah of the Mikdash or Kodshim.

(Gemara - R. Yosi of the south, to R. Yonah): The Mishnah should teach oppositely! If so (the outer goat of Yom Kipur atones for more than Se'irei Rosh Chodesh), Se'irei Rosh Chodesh may be offered on Yom Kipur, for we ascend in Kedushah, and we do not descend - but how can Se'irei Yom Kipur be offered on Rosh Chodesh? We do not descend in Kedushah!

Answer (R. Lazar citing R. Bun): Our Mishnah is fine. [Rabanan asked that goats] of Yom Kipur may be offered on Rosh Chodesh for they atone their Kaparah, and the Kaparah of Rosh Chodesh. However, [goats] of Rosh Chodesh cannot be offered on Yom Kipur, for they atone only their own Kaparah!

If someone ate five k'Zeisim of Chelev [in separate He'elamos] and separated [and offered] four Korbanos, and thought that they are five, perhaps he atoned [for the fifth?! Surely he did not!] If someone ate four k'Zeisim of Chelev and separated [and offered] five Korbanos, all the more so he atoned!

So R. Shimon used to say that 32 goats are offered for the Tzibur every year; 31 are outside (the outer Mizbe'ach) and are eaten, and one is inside and is not eaten, and the Se'ir ha'Mishtale'ach [is sent, but not offered];

Twelve are offered for the 12 months (every Rosh Chodesh), eight during Sukos, seven on Pesach, two on Shavu'os - one due to [Musaf of] the day, and one due to [Shtei] ha'Lechem, one on Rosh Hashanah, and one on Yom Kipur.

Once Moshe heard this, he said "if so, one who has a Safek Aveirah must bring all of these Korbanos!" (It is not clear why he should need to bring all of them. It seems that the Torah obligated each one to atone for Aveiros after the previous! Based on Kabalah, each Korban fixes a different matter.)

(R. Tanchuma citing Reish Lakish): When Hash-m told Moshe "v'Hisvadah Alav..." (Se'ir ha'Mishtale'ach atones for everything), he began and said "Mizmor l'Sodah", based on "v'Hisvadah Alav."