The Mishnah teaches us:
The daily offering is sacrificed and its limbs are carried by nine priests, as mentioned in a previous mishna. These nine carry the limbs and the accompanying libations and meal-offerings. Occasionally, the service is performed by ten priests, occasionally by eleven, and sometimes by twelve priests; no fewer than nine and no more than twelve.
The Bartenura in his commentary on this Mishnah explains:
on every day, nine [priests]; six for the limbs and the innards, as we stated above (Mishnah 3) and one for the fine flour, and one for the baked cakes and one for the wine.
The Yerushalmi Yoma 2:4 explains similary:
The daily sacrifice is brought by nine persons, by ten, by eleven, by twelve, neither less nor more. How is this? Itself by nine.Plus the four who precede the presentation of the daily sacrifice makes 13., and on Tabernacles in the hand of one a vial of water, these are ten120Together 14.. In the evening by eleven; itself by nine and in the hands of two, two wooden logs. On the Sabbath by eleven, itself by nine, two, in their hands two cups of incense of the shew-bread;.. On the Sabbath of Tabernacles, in the hand of one a vial of water.
A he-goat is brought by eleven, the meat by five, the intestines, and the fine flour, and the wine, each by two.
A bull is brought by twenty-four, head and leg, the head by one and the leg by two; spine and leg, the spine by two and the leg by two; breast and fat, the breast by one and the fat by three; the two front legs by two; the two side pieces by two; the intestines, and the fine flour, and the wine by three each. When has this been said? For a public offering. But for a private offering, if one wants to sacrifice, he sacrifices. Skinning and cutting into pieces is the same for these and for those.
Rabbi Adin Even-Israel Steinsaltz ZT"L explains:
Obviously, any “special events” that were going on on a given day would affect the number of kohanim that were needed. The Mishna teaches, for example, that the korban tamid, which was the first sacrifice brought every day, was brought by nine, ten, eleven or twelve kohanim, depending on the day.
The English explanation on the Mishnah explains:
[The offering] itself by nine; In mishnah three we learned that it took nine priests to carry the various parts of the tamid offering up the ramp and then afterwards from the ramp to the altar. This referred to the morning tamid offering. As we shall see below in section four, the evening tamid required two more priests.
At the festival [of Sukkot] in the hand of one a flask of water, behold there were ten. On Sukkot at the morning tamid they would also offer a water libation. We shall learn more about this water libation when we study Tractate Sukkah.
In the evening by eleven: [The offering] itself by nine and in the hands of two men were two logs of wood. The evening tamid, offered at dusk, required eleven priests. Nine to carry the offering itself and two to carry about two logs of wood to add to the altar’s fires. They also added wood in the morning, but in the morning the wood was added by the priest who cleaned out the old ashes (see above mishayot 1-2). This was done before the tamid was offered.
On Shabbat by eleven: [The offering] itself by nine, in the hands of two men two handfuls of incense for the showbread. On Shabbat the morning tamid also required eleven priests. Nine to offer the sacrifice itself and two to carry the incense which was offered every Shabbat in honor of the outgoing showbread (see Leviticus 24:6-7).
There is even a Gemara that explains that sometimes, there were 17 Kohanim who perfomed the service (Yoma 26b):
The Gemara asks with regard to Rabbi Ḥiyya’s statement: But wasn’t it taught in a baraita that sometimes there are seventeen priests involved in the daily offering?
And see the explanation given by the Rosh Kollel of Kollel Iyun Hadaf of Yerushalayim: Rabbi Mordecai Kornfeld of :
RASHI explains that the Beraisa counts all of the Kohanim who were selected by the Payis to perform an Avodah specifically related to the Korban Tamid. The Avodah of the Machtah was not an Avodah related to the Korban Tamid, but to the Ketores. (In this case, two separate Payesos were conducted to select the Kohanim for the Avodos related to the Korban Tamid. The first 16 Kohanim were selected with the first Payis, and the Kohen who would bring the Evarim from the Kevesh to the Mizbe'ach was selected by the fourth Payis.)
An Avodah that is unrelated to the Korban Tamid (such as the Machtah) is not included in the Beraisa's count of Kohanim. Thus, the Beraisa which says that 17 Kohanim were selected cannot follow the view of Rebbi Eliezer ben Yakov, because he says that no Payis was done to select a Kohen to bring the Evarim to the Mizbe'ach.
The Rishonim reject this explanation. Whether or not the Beraisa follows Rebbi Yehudah is irrelevant. Even if the Beraisa disagrees with Rebbi Yehudah and maintains that an extra Kohen was selected by the Payis to bring the Machtah, that Avodah cannot be included in the count because it is not related to the Korban Tamid.
The Tosfos on this Gemara explains the following
Implied question: The Reisha of the Reisha says that 13 Kohanim merited in it (the Tamid, and according to Rabanan, there are 14 including the one who brings limbs from the ramp to the Mizbe'ach
Answer: We can answer that it is even like Rabanan. We count only the 13 who merit in the second lottery. The one who brings limbs from the ramp to the Mizbe'ach is in the fourth lottery by itself.
And:
Explanation #1: Rather, because we want to say "no less and no more", we say that no one holds that it is offered with less than nine. However, [even Rabanan hold that] it is not always 10;
"it is offered wiht not less than nine"- this seems to be the opinion of the Tosfos, but can also be found in the Gemara (Yoma 26b) "The daily offering itself is sacrificed by nine".
See the commentary of Steinsaltz on this Gemara:
בין הערבים בכל יום היו באים אחד עשר כהנים, כיצד? הוא קרבן התמיד עצמו היה נעשה בתשעה, ושנים נוספים שבידם שני גזירי עצים שהיו מניחים על המזבח, ומצות נתינת שני עצים על המזבח מיוחדת לבין הערבים בלבד. בשבת היה בא באחד עשר, כיצד? הוא עצמו בתשעה, ושנים נוספים שבידם שני בזיכי לבונה של לחם הפנים שאותם היו מקטירים ביום השבת. ובשבת שבתוך חג הסוכות נוסף להם עוד כהן כי ביד אחד צלוחית של מים לניסוך המים, הרי בסך הכל שנים עשר.
So, based on the above, there were not less than 9 kohanim performing the services in the Beis HaMikdash. However, the Yerushalmi cited above says that the daily sacrifice is brought by 9,10,11 or 12. But no less or more. This I find puzzling, since the Tosfos writes:
וגירסת הספרים ודלא כר' יהודה נ"ל לפרש והתניא י"ז פי' בכל בוקר היה י"ז לכל הפחות ולא משכחת לה אא"כ חשבת כל הכהנים הזוכין בכל הפייסות
The text in all Seforim is "and not like R. Yehudah." I explain the question "a Beraisa says 17", i.e. every morning there were at least 17, and we find this only if you count all the Kohanim who merit in all the lotteries (source for English translation).
So, to summarize, it seems to me that in the Gemara, there are different opinions, but the Tosfos seems to say that there were, on a regular day, 17 Kohanim performing the services, not only the Avodos of the Tamid, but all Avodos.
