It is written in Shulchan Aruch Orach Chaim 66:1 that one may not sit a sukkah on Shemini Atzeret (Simchat Torah in chutz la'aretz) because it looks like bal tosif. Does this also apply to women? Can they transgress bal tosif if the are not commanded in this mitzvah?
Let me share with you some of my thoughts about this sugya, will be happy to hear some critiques:
About women transgressing Bal Tosif when they do a time-bonded mitzva, there is a discussion between Rashi (Rosh Hashana 33a d"h Ha Nashim) and Tosfot (Eruvin 96a d"h Michal), according to Rashi, when she does a time-bonded mitzva with intention to fulfill it, she transgresses Bal Tosif and according to Tosfot, she does not. The acharonim discusses what is behind Rashi and Tosfot opinion, the Kovetz Shiurim (Baba Batra 54) writes that according to Rashi, when a woman does a time-bonded mitzva is considered a "maase mitzva" (mitzva act), and according to Tosfot it is not, so that's why it also does not transgress Bal Tosif.
Kovetz Shiurim in Pessachim piska 166 discusses if in order to transgress the issue of Bal Tossif when someones does a mitzva after its time, if it needs (besides intention to fulfill the mitzva**) only that the "maase mitzva" (act of the mitzva) be OK or if it needs that if one would do this in the proper time, he would fulfill the mitzva.
So, according to Tosfot is clear that in the case you presented she does not transgress Bal Tosif [there is neither "kium mitzva" (fulfillment of the mitzva) nor "maase mitzva" (mitzva act)] , but according to Rashi (with Kovetz Shiurim understanding) it depends on discussion the Kovetz Shiurim brings up in Pessachim (last paragraph), since there is a perfect "maase mitzva" but if it would be in the proper time the mitzva would not be fulfilled since there is no "kium mitzva" (fulfillment of the mitzva).
** If there is no intention to fulfill the mitzva, is only "looks like Bal Tosif", see Massechet Rosh Hashana daf 28 and (more explicitly) Korbal Netanel on the Rosh on Sukkah Perek 4 Siman 7.