80a (Mishnah - R. Eliezer): If blood that requires four Matanos (being thrown against walls of the Mizbe'ach) was mixed with blood that requires one, we do four Matanos;

R. Yehoshua says, we do one Matanah.

R. Eliezer: You transgress Bal Tigra (detracting from a Mitzvah)!

R. Yehoshua: You transgress Bal Tosif (adding to a Mitzvah)!

81a (Rava): R. Eliezer views blood put in the wrong place as if it were water (he permits, so we can fix the other Korban), Chachamim do not.

Rosh Hashanah 28b (Abaye): (If you hold that one is Yotzei without intent,) one who sleeps in a Sukah on Shemini Atzeres is lashed for Bal Tosif!

Rava: I say that Bal Tosif only applies at the time of the Mitzvah.

Question (Rav Shemen bar Aba - Beraisa): If a Kohen decided to add another Berachah to Birkas Kohanim, e.g. "Hash-m... should bless you 1000 times", he transgresses Bal Tosif (even after the time for the Mitzvah passed)!

Answer: If another Tzibur (that was not yet blessed) would present itself, he could bless again, so the entire day is the time for the Mitzvah.

Support: R. Yehoshua holds that Bal Tosif applies even after the Mitzvah was finished (the Bechor's blood needed only one Zerikah). This is because if there would be another Bechor to offer, we would throw its blood, so the entire day is the time for the Mitzvah!

Rejection: Perhaps R. Yehoshua holds that Bal Tosif applies even after the time for the Mitzvah.

(Rava): One transgresses Bal Tosif at the time of the Mitzvah even without intent, and not at the time of the Mitzvah only with intent.

Rif and Rosh (Megilah 15b and 3:17): A Kohen may not add a Berachah to the three Berachos of Birkas Kohanim, such as "Hash-m... should bless you 1000 times", whether silently or aloud, for it says "Lo Tosifu." We say that if another Tzibur would present itself, he could bless again. This shows that if a Kohen gave Birkas Kohanim here, and went elsewhere where they did not yet give Birkas Kohanim, he may give Birkas Kohanim with them.

Rambam (Hilchos Tefilah 14:12): A Kohen may not add a Berachah to the three Berachos of Birkas Kohanim, such as "Hash-m... should bless you 1000 times", whether silently or aloud, for it says "Lo Tosifu."

Tosfos (Rosh Hashanah 16b DH v'Tok'im): Why may we blow extra Teki'os? This is Bal Tosif. One transgresses even without intent, for the entire day is a Mitzvah if another Tzibur that did not yet hear them will present itself! We must say that repeating a Mitzvah is not Bal Tosif.

Pri Megadim (Petichah Koleles to Shulchan Aruch, 1:38): Tosfos agrees to the Rashba (below) that anything done for a fence, e.g. Yom Tov Sheni, is not Bal Tosif. He asked only about Teki'os, which are not a fence, rather, to befuddle the Satan. Beis Din may partially detract from a Mitzvah, but not totally uproot a Mitzvah. Therefore, they did not decree (due to concern lest one fix a musical instrument) never to blow the Shofar

Rashba (Rosh Hashanah 16a DH Lamah): Bal Tosif is what a person decrees on his own. An enactment of Chachamim is not Bal Tosif. This is why we sleep in the Sukah on Shemini Atzeres. We are obligated to follow their words!

Pri Megadim (ibid., 40): According to Tosfos, Bal Tosif does not apply to repeating a Mitzvah. This explains why we may light additional Neros Chanukah (letter of the law, one is Yotzei through one Ner). The Rashba and those who say that it applies to repeating a Mitzvah must hold that Bal Tosif does not apply to Mitzvos mid'Rabanan. Even though the Rambam says that mid'Rabanan Mitzvos are Torah law due to "do not veer from what Chachamim tell you", this refers to fences, but not to enactments such as Ner Chanukah and Mikra Megilah. He says (Hilchos Mamrim 1:2) that "do not veer" applies to fences

Minchas Chinuch (454 DH v'Hinei ha'Rav and 455 b'Sof): The Rambam does not mention lashes for Bal Tosif. This is because we hold that Mitzvos need intent, so one transgresses Bal Tosif only with intent. If he thinks that he is doing a Mitzvah, he errs, and he is not worthy of lashes. If he perverts Torah, he is an Apikores whom we throw to a pit! He must explain that when the Gemara discusses lashes, this is mid'Rabanan. Sefer ha'Chinuch says that one is lashed mid'Oraisa. He must hold that that Mitzvos do not need intent, so one transgresses Bal Tosif even without intent.

Pri Megadim (ibid., 37): It is difficult to say that when the Gemara discusses lashes, this is mid'Rabanan

Shulchan Aruch (OC 128:28): If a Kohen gave Birkas Kohanim and went to another Beis ha'Keneses and found a Tzibur that did not yet reach Birkas Kohanim, he may give Birkas Kohanim again.

Magen Avraham (40): Repeating a Mitzvah is not Bal Tosif.

Torah Temimah (Devarim 4:2): Why should the Torah forbid a Kohen to give extra Berachos? It seems that Bal Tosif is lest one come to think that Shi'urim of the Torah are optional, and he come to detract. This is why the Rashba says that we are not concerned for enactments of Chachamim. Also, we are not concerned regarding mixtures, for one realizes that he adds (e.g. extra Zerikos) due to the mixture, and he will not come to detract. This also explains why some say that one transgresses only if he intends to add.

Suggestion: The Rambam holds that there are no lashes for Bal Tosif is because it is a Lav shebi'Chlalos (one Lav that forbids multiple things). Granted, if Bal Tosif includes a new Mitzvah that one invented, this is Lav shebi'Chlalos. However, if it applies only to adding to existing Mitzvos, why is this Lav shebi'Chlalos? The Rambam obligates lashes for Kodshim that became Pasul due to "do not eat any abomination", for it is as if this Lav was said about every Pesul by itself. Likewise, it is as if Bal Tosif was written about every Mitzvah! Rather, Bal Tosif applies even to a new Mitzvah.

Rebuttal (Igros Moshe 1:14:2): If Bal Tosif applied to a new Mitzvah, this would be because one may not add to the Torah's obligations, e.g. a new festival or to take a stick. The actions themselves are permitted, but one may not add. This is not one Lav forbidding many matters, rather, one matter from which come many Isurim. We find a bigger Chidush, that one is lashed for eating a Tamei animal, fish or fowl, even though many species are included. Since the Torah did not divide the Isur, the different species are details of one Lav.

Pri Megadim (ibid., 1:39): The Halachah follows R. Yehoshua, who says that at the time of the Mitzvah, Bal Tosif applies, even if he intends 'the extra Zerikos of blood are like water.'

Yom Tru'ah (Rosh Hashanah 28b DH Mesiv): The case of Birkas Kohanim teaches that Bal Tosif applies even to mere Dibur. However, since he intends to add his own Berachah, surely he intends to transgress. Why is this difficult only for Rava, who says that Mitzvos do not need intent? Also, the Kohen does not say that the addition is mid'Oraisa. The Rambam says that one transgresses only if he says that the addition is mid'Oraisa! It seems that this is only for matters added for a fence. In general (e.g. Hilchos Tefilah 14:12), he agrees that intent to add suffices to transgress.

Chasdei David (Korbanos 8 DH Chachim p.135): If one does a Mitzvah and adds the same Mitzvah, e.g. another pair of the same Tefilin, he transgresses Bal Tosif only if he intended. Without intent, it is forbidden mid'Rabanan. He was Yotzei the Mitzvah, even if he tied them together; if the Mitzvah need not be bound, it is as if they are separate. If he added a part of the Mitzvah, e.g. a fifth Parshah in Tefilin, whether he repeated a Parshah or fabricated a new Parshah, he transgresses Bal Tosif and he was not Yotzei the Mitzvah, because they are tied. At the time of the Mitzvah, this is even without special intent. If they are not tied, he transgresses only with intent, but he was Yotzei. Stam, it is Asur mid'Rabanan; if it is evident that he does not intend to add, it is permitted l'Chatchilah. The same applies to Mitzvos of speech or actions. When he clearly does not intend to add, it is permitted with the same or a different species. Wearing two pairs of Rashi or two pairs of R. Tam Tefilin is like doing the Mitzvah twice. Sitting in a Sukah on Shemini Atzeres is permitted in Eretz Yisrael with a Heker (indication that it is not l'Shem Mitzvah, e.g. he makes Kidush in the house), and in Chutz la'Aretz without a Heker, like Tefilin. If Beis Din ruled to add to an Aseh or Lav, and said that this is Torah law, they transgressed Bal Tosif, but they are not lashed. If they made a fence or say to do so due to Safek, it is permitted and we are commanded to obey. They may detract from Torah law only temporarily through an action, or passively, even for generations.