In the last post I did on bal tosif I left a question hanging that I will try to return to bl”n, but first this...
The Rambam (Lulav 7:7) writes that one may take extra hadasim with the lulav because having a full bouquet looks more beautiful. However, one may not take more of the other minim; taking an extra lulav, esrog, or aravah does not add to the beauty of the mitzvah and violates bal tosif. The Ra’avad disagrees and writes that he does not understand why taking extra minim disqualify the mitzvah. Since lulav does not require eged, meaning there is nothing which unites whatever you pick up and defines it as a single halachic bundle, there is no connection between the extra items picked up and the items which are part of the mitzvah requirement. An extra lulav, esrog, or aravah serves no function and has no effect on the character of the mitzvah.
Recall our discussion before Rosh haShana regarding bal tosif: according to the Rambam bal tosif occurs when adding chiyuvim; e.g. were Chazal to give the impression that a din derabbanan is actually a chiyud d’oraysa they would be in violation of bal tosif. Ra’avad sees bal tosif as a function of changing a kiyum mitzvah, e.g. adding an extra bayis to tefillin.
The Avi Ezri extends that discussion to explain our machlokes as well. According to the Rambam whether or not the extra items technically count as part of the cheftza shel mitzvah bundle of 4 minim is irrelevant -- the disqualification of bal tosif is caused by the attempt by the person to alter the chiyuv of the mitzvah by adding minim. The Ra’avad who looks only at the kiyum mitzvah as the measure of bal tosif sees no problem in this case because since there is no eged the kiyum mitzvah is unchanged.