It is forbidden to add onto the mitzvot. This includes extending a mitzva in time (such as adding an extra day to a holiday), increasing its quantity (such as adding a fifth species to one’s lulav, or a fifth biblical text inside one’s tefillin), or creating a new mitzva. An obvious question arises: how then could our Sages prohibit actions that were not prohibited by the Torah, such as eating chicken with milk?
Some answer that the prohibition of Bal Tosif applies only if those making an addition claim that it is a mitzva in the Torah. No one ever claimed that eating chicken with milk is biblically prohibited.
Others state that the law of Bal Tosif applies only to adding positive commandments. In contrast, our Sages were allowed to prohibit additional things. This answer, though, does not explain how the Sages were permitted to create the holidays of Purim and Chanukah.
An example of extending a mitzva in time is sitting in the sukkah on Shmini Atzeret, the day which follows Sukkot and on which there is no mitzva to sit in the sukkah (at least in Israel; it is more complicated in the Diaspora). Some Rishonim write that one may do so if he makes sure there is a heker, something unusual, to make it clear that he is not trying to fulfill a mitzva. Along the same lines, Rav Kook states that a heker was necessary for the rabbinically-added holidays, so no one could confuse them with biblical mitzvot. Thus, Purim is celebrated on different dates depending upon whether or not one lives in a walled city. There is no comparable rule for any other mitzva. And Chanukah lighting has different levels of observance – the minimal requirement, the enhanced level, and the extra-enhanced level. This too is unique.
Two types of additions do not constitute a problem of Bal Tosif according to most opinions. One type is adding in frequency. For example, performing the same mitzva numerous times a day is not prohibited. A second type is broadening the ranks of those who perform a mitzva. For example, a woman is allowed to perform a mitzva from which she is exempt. Nevertheless, there is an opinion that even these two types transgress the prohibition of Bal Tosif, if the person performing an extra mitzva mistakenly believes the Torah mandates it.