A few years ago in honor of the occasion of my MIL's donation of a sefer torah, my wife’s uncle edited and published a small collection of the correspondence and writings of my wife’s grandfather, HaRav Dov Yehudah Shochet, who was among the talmidim muvhakim of Telz (see my BIL's article on Telz) and a Rav in Basel, the Hague, and Toronto, and in whose memory (along with others) the sefer was written. By coincidence, one of the few full length shiurim (I only recently got my hands on the kuntres) is devoted to the topic of bal tosif which we have been discussing as of late. I am sorry I can only write up a smattering of an idea from this brilliant shiur (and I am adapting the idea, so the errors are mine); the small amount printed is rav b'eichus on many levels despite being miyut b'kamus, and I hope bl"n to share more.
The shiur draws a distinction between two types of bal tosif: changing the tzurah of an existing mitzvah vs. fabricating a new mitzvah. (This is similar to the distinction I cited from Avi Ezri between adding a chiyuv vs. changing the kiyum mitzvah.) As we learned, the Rashba writes that takanos of Chazal do not violate bal tosif because they are justified by the need for legislation. The Turei Even asks: the gemara (R”H 28) writes that R’ Eliezer holds if the blood of a korban requiring the sprinkling of dam 4 times gets mixed with the blood of a korban that requires sprinkling only once, sprinkling the blood 4 times is prohibited because of bal tosif. Why doesn't the need to perform zerikas hadam 4 times not override the issur of bal tosif just like the need to enact a takanah overrides bal tosif? Based on the distinction between the two types of bal tosif, this question is easily answered: given the need for legislation, creating new takanos does not violate bal tosif; however, no matter what the need, the parameters of an existing mitzvah cannot be altered. Because one of the korbanos demands zerika no more than one time, the mitzvah of zerika cannot be modified and done four times.
Is adding tekiyos d’meyushav an addition of a new mitzvah or a change to the existing mitzvah of tekiyas shofar? That essentially is the difference between Rashba, who justifies tekiyos d’meyushav as a takanah and therefore excluded from bal tosif, and Tosfos, who suggests a different sevara and explains that doing a mitzvah 2 times is allowed. The question I ended my last discussion of this topic with (see this post) -- why does the Rashba's sevara not answer Tos' question -- does not get off the ground. Tosfos could not use the Rashba’s sevara because changing the parameter of an existing mitzvah, as opposed to adding a new takanah, would be a kum v’aseh violation of bal tosif which Chazal have no license to do.
We can explain the debate on a deeper level by returning R’ Akiva Eiger’s question (which we discussed here) on Tos’ comparison of tekiyos d’meyushav to a kohein doing birchas kohanim for a second time in one day. R’ AK”E argues that there is an obvious difference: the kohein has a new chiyuv of birchas kohanim every time he enters a shul that is up to duchaning; the ba’al tokeya has no new chiyuv to blow shofar once he has fulfilled his mitzvah d’oraysa. Chasam Sofer answers that the ba’al tokeya’s obligation of shofar is in fact incomplete by dint of arvus so long as others still have not heard shofar.
Tosfos may have held like the Chasam Sofer and viewed tekiyos d’meyushav as an extension of the mitzvah of tekiyos already in progress. The Rashba, however, may have sided with R’ Akiva Eiger and viewed tekiyos d’meyushav as a new mitzvah, the old mitzvah of tekiyos already having been completed with the conclusion of one round of tekiyos.