There is a Halachic principle mentioned in the Talmud called "Ein Osin Mitzvot Havilot Havilot," which literally means, "One should not perform Mitzvot in bunches." Each Mitzva deserves individual attention, and one therefore should not combine multiple Mitzvot into a single performance. He should instead perform each Mitzva separately, in order to afford it the honor and respect it deserves.
Rabbi Avraham Palachi (Turkey-Israel, 19th century), in his work "Va'ya'an Avraham" (Orach Chayim, 50), establishes a fundamental rule concerning the principle of "Ein Osin Mitzvot Havilot Havilot." Namely, this prohibition applies only to fulfilling multiple Mitzvot by performing multiple acts simultaneously. For example, the Gemara speaks of a case of a Kohen who gives the Sota waters to several women at the same time, and of a Kohen who sprinkles the purifying waters on several Temei'im (people who ritually impure) simultaneously. In both these cases, the Kohen fulfills two Mitzvot at one time by performing two simultaneous actions. Where, however, a person performs a single action which fulfills multiple Mitzvot, this prohibition does not apply.
Rabbi Palachi posits this rule amidst his discussion of the question of whether one may conduct a single Siyum (meal celebrating the completion of a Talmudic tractate) upon the completion of two Masechtot (tractates) of Talmud. At first glance, this would transgress the prohibition of "Ein Osin Mitzvot Havilot Havilot," in that a number of Mitzvot are combined into a single context. But Rabbi Palachi rules that one may conduct a single Siyum for several Masechtot, because, as explained, the prohibition applies only to multiple actions performed simultaneously. In this case, one conducts one meal whereby he performs several Mitzvot, and thus no prohibition is entailed.
By the same token, one may conduct a Siyum at a Shabbat meal, or eat a Shabbat meal as the "Se'udat Mitzva" of a Berit Mila or Sheva Berachot celebration. In all these cases, a single action fulfills two Mitzvot, and thus the prohibition of "Ein Osin Mitzvot Havilot Havilot" does not apply.
Another example of this rule is the Halacha mentioned in the Talmud Yerushalmi allowing one to use "Shemen Sereifa" for kindling the Chanukah candles. "Shemen Sereifa" is oil that had been designated as Teruma (portion of one's produce given to the Kohen) but subsequently became Tamei. There is a Mitzva to burn "Shemen Sereifa," and thus by burning this oil with Chanukah candles, one fulfills two Mitzvot: kindling the Chanukah candles, and burning "Shemen Sereifa." Here, too, a single action fulfills two Mitzvot, and it is therefore permissible.
Likewise, the Gemara in Masechet Pesachim establishes that a Kohen may fulfill the Mitzva to eat Matza on Pesach by partaking of Matza produced from Teruma. Through the single act of consuming Matza he fulfills the Mitzva of Matza as well as the Mitzva of eating Teruma. Since he fulfills two Mitzvot in a single act, no prohibition is violated.
Finally, Chacham Ovadia Yosef, in his work Chazon Ovadia (Hilchot Yom Tov, pp. 94-95), applies this rule to the consumption of bread when the first night of Pesach or the first night of Sukkot falls on Friday night. In such a case, a person is obligated to partake of a Ke'zayit of bread (or Matza) by force of two Mitzvot: the Mitzva to eat Matza (on Pesach) or to eat in a Sukka (on Sukkot), and the Mitzva to eat a meal on Shabbat. The Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1833-1909), in his work Hod Yosef (61), ruled that one must therefore partake of two Ke'zayit-amounts of bread/Matza in this case. He held that due to the principle of "Ein Osin Mitzvot Havilot Havilot," one may not fulfill two Mitzvot with the consumption of a single Ke'zayit. Chacham Ovadia, however, disagrees, in light of the rule we have discussed. The prohibition of "Ein Osin Mitzvot Havilot Havilot" does not apply to performing multiple Mitzvot through the performance of a single action, and therefore it is permissible to eat one Ke'zayit to fulfill both the Mitzva of Matza or Sukka, and the Mitzva to eat a Shabbat meal.
Summary: It is permissible to fulfill several Mitzvot through the performance of a single action. Thus, one may hold one Siyum celebration for two or more Masechtot, or combine a Siyum or another Se'udat Mitzva – such as the meal after a Berit Mila – with the Shabbat meal. Likewise, when the first night of Sukkot or Pesach falls on Friday night, one may eat a single Ke'zayit of bread or Matza to fulfill both the obligation of Sukka or Matza and the Mitzva to eat a Shabbat meal.
