At first glance it would seem that we can derive the principle of “Ein me’arvin simcha besimcha” (“We do not celebrate two happy events simultaneously”) from a verse in Parshat Vayetze. Lavan said to Yaakov, “Complete the week of this one and we will give you the other one too (to marry)” (Bereishit 29:27). We see that each happy event should be celebrated individually. However, the Talmud (Moed Katan 9a) derives this principle from the behavior of Shlomo at the dedication of the Beit HaMikdash. He made sure that the week-long dedication of the Temple did not overlap with the week-long holiday of Sukkot. Instead, there were fourteen consecutive days of celebration (1 Melachim 8:65).
There is logic behind this rule. Someone who is celebrating two occasions at the same time cannot fully focus on either one. This is why we do not have weddings on Yom Tov or Chol HaMo’ed (the intermediate days of a festival). An interesting question arises. May we have weddings on Purim? If the rule is derived from Shlomo’s behavior, it is possible that the prohibition of mingling celebrations is only relevant to biblically mandated celebrations (such as Sukkot, when the Torah commands: “You are to rejoice on your festival”); it would not be relevant to Purim, which is rabbinic. On the other hand, if we derive this principle from Lavan, it would apply to rabbinically mandated celebrations. After all, the joy during the seven days following a marriage is rabbinic, and yet we see that Lavan (with Yaakov’s agreement) was careful not to mingle the celebrations.
In practice, this principle was accepted only with regard to weddings. Other celebrations, such as the festive meals accompanying a circumcision or a Pidyon HaBen (redemption of the firstborn), take place even on festivals. This difference may be because the celebration of a marriage is considered the most joyful of all celebrations. An indication of this status is that it is only for a wedding that we make the blessing of “SheHaSimcha BiMe’ono.”
Despite this rule, according to Torah law a man may marry several women at the same time under the same chupah (wedding canopy). Additionally, according to the letter of the law, a number of couples could be married under the same chupah (if not for the fear that doing so would cause enmity and jealousy between the families involved). It would seem then that the problem of “Ein me’arvin” is limited to cases when there are two different types of events being celebrated, as is the case with having a wedding on Yom Tov. In contrast, when the celebrations are of the same type, this principle would not apply.
Based on this, it would seem that Yaakov could have married Leah and Rachel on the same day, as long as each couple could have their own sheva berachot celebrations.