לע"נ ר' מרדכי גימפל בן אברהם משה
A] There is a "famous" Tosfos [definition: Tosfos that I learned] in Rosh Hashana [כח: ד"ה ומנא תימרא] that talks about the איסור of בל תוסיף. They say that doing a mitzva more than once is NOT בל תוסיף. They add that the same applies to lulav. Only if he adds another species does he transgress the prohibition but not if he adds a second lulav or more hadassim and aravos. [See Minchas Chinuch mitzva 454/4 who wonders how Tosfos compares doing a mitzva twice to adding to the number of lulavim. The former is not בל תוסיף while the latter may well be עיי"ש].
Tosfos [at the end] tries to prove that one may add to the requisite number of Aravos from the law of succah where all one is required to build is two walls and a third that is only a tefach and still if a person builds four complete walls he is not עובר on בל תוסיף. Tosfos rejects this and says that there is no proof from Succah because the added wall[s] enhance the Succah as they make it more תשבו כעין תדורו.
עומק דברי התוספות - There is no specific number of walls that the Torah requires. The halacha of two regular walls and a third a tefach long is what makes the Succah meet the requirement of תשבו כעין תדורו - the Succah becomes like one's home. If he builds four complete walls he is NOT adding on to the fundamental obligation of the Torah. He is just meeting the requirement of תשבו כעין תדורו in an enhanced form. IF the obligation of the Torah was 3 walls and he built a fourth then we may have a problem but that is not the case.
B] We see from Tosfos that the wall is a חפצא דמצוה - a bonafide mitzva object. Otherwise there would be no בל תוסיף to talk about. This is significant because there is a machlokes rishonim if the wall is a חפצא דמצוה - See Rabbi Genack Shlita in his Gan Shoshanim [סימן לה].
C] One contemporary sefer wanted to suggest that Tosfos accords with the Shlah who says that building four walls is a הידור מצוה. However, MaRan HaRav Hutner in his shiurim on Succah [סימן ד and Rav Yaakov Chaim Sofer in his עוז יעקב] correctly points out that Tosfos never calls it a הידור מצוה - just more תשבו כעין תדורו. When the gemara in Shabbos [קלג] gives examples of הידור מצוה it significantly omits the notion of building a fourth wall for the Succah.
D] The mishna in Tomid says that the Kohanim would guard in three specific places. Rav Moshe Rosen [who was the Rav of the town where the Chazon Ish lived and they had a chavrusa together. He penned a multi-volume set on shas] asks why a specific number is given. Just tell me the places and I can count how many there are?! He suggests that that mishna is telling us that if the kohanim guard in more than three places it would be בל תוסיף. Rav Tzvi Pesach Frank [הר צבי פרשת במדבר] rejects this based on our Tosfos. Having more than three places guarded is not בל תוסיף but enhanced שמירה just as more walls is not בל תוסיף but enhanced תשבו כעין תדורו.
Halacha li-maaseh - Ideally one's Succah should have four walls either because it is more תשבו כעין תדורו or because it is hiddur mitzva. So paskens the Chaye Adam and others [See עוז מלכו סי' ח].
Torah is GESHMAKKKKK!!!!!
See here where this Tosfos is expanded upon with Hashem's limitless help....
עיין עוד בספר משנת חיים ע"ס דברים סי' עא לג"ר חיים מאיר הלוי שטיינברג שליט"א
