Q: Why do we list only seven Noahide commandments?
Q: Why do we list only seven mitzvot that Noahides are required to perform? If a Noahide observes the Shabbat, he or she is performing more than the seven mitzvot.
A: The term "Seven Mitzvot of Bnei Noach" appears in a Baraita in the Tractate Sanhedrin, where there is a list of the seven mitzvot – six main prohibitions and the requirement to establish courts of justice. According to one source in the Talmud there are in all thirty commandments (Chulin 92), and there is a discussion as to the details of these thirty mitzvot. Rabbi Aaron Lichtenstein (from the United States, a cousin of Rabbi Aharon Lichtenstein of Alon Shevut, in Israel) lists sixty-six mitzvot in all. The "seven" mitzvot can be viewed as seven general principles or categories of commandments, in the same way as the Ten Commandments include all 613 of the mitzvot that the Jews were commanded to observe.
According to Rav Nissim Gaon, Bnei Noach are obligated to perform all the mitzvot that their logic would lead them to do. But this raises a problem: some deeds which seem appropriate and reasonable in some societies are perceived as unreasonable by other societies. Therefore these mitzvot do not appear in the standard list.
We definitely accept that Noahides are allowed to take on an obligation to perform other mitzvot. But the Holy One, Blessed be He, did not require them to do so, and such "volunteer" deeds therefore do not appear in the list of mitzvot.