The Mishna in Nedarim tells us that one cannot take a shavua to do or not do a mitzvah or issur because one is already mushba m’har Sinai, bound by oath from mattan Torah to obey mitzvos, and one shavua cannot be chal on top of another pre-existing shavua. However, one can take a neder on a mitzvah – e.g. one can take a neder from sitting in sukkah even though one is already bound to do the mitzvah of yeshivas sukkah. The difference is that a shavua is an issur gavra – it relates to the act of sitting in sukkah, in direct contradiction to the Torah’s command; a neder is an issur cheftza – it addresses the sukkah as an object, but does not directly address the mitzvah act of sitting in sukkah.
A neder is made through hatpasa, saying X is assur like Y, where Y is something that one has created an issur on by a neder or some other declaration, e.g. hekdesh. One can take a neder not to eat food on day X just like one does not eat on day Y, provided day Y is one which has previously been demarcated as a fast day though a neder. The gemara (Shavuos 20b) discusses a more complicated case where day Y is the day on which Gedalya ben Achikam was killed - even though one would not eat on that day anyway because it is a fast day, if one also took a neder not to eat on the day of Tzom Gedalya, it can serve as a term of hatpasa for the neder saying day X is like that day. How does this neder not to eat on Tzom Gedlaya work? Rashi writes that just as a neder is chal on sukkah because it creates an issur cheftza, so too, the neder adds an issur cheftza to the prohibition of Tzom Gedalya which already exists. Tosfos disagrees with Rashi's blanket rule and holds (based on a girsa change rejected by Rashi) that this chiddush is true only by issurei derabbanan like Tzom Gedalya, but not by issurei d’oraysa. If one were to take a neder not to eat neveila or not to eat on Yom Kippur, according to Rashi such a neder is chal; according to Tosfos it is void.
Returning to the discussion from last week re: issurei gavra and issurei cheftza, perhaps this is the issue here. According to Rashi, all issurim, both d’oraysa and derabbanan, e.g. Tzom Gedalya and issur neveila, are issurei gavra, and a neder is chal on top of them to add an issur cheftza. According to Tosfos, only issurei derabbanan are issurei gavra, but issurim d’oraysa like neveila and achila on Y”K are issurei chaftza which a neder adds nothing to and cannot be chal on. A middle position is taken by R’ Akiba Eiger (Y”D 215:6): neveila is an issur cheftza which a neder cannot be chal on, but Yom Kippur is an issur gavra, as it is the day which creates a temporary issur, but the food is fundamentally heter.