Gemara

(Rava): One who offers limbs of a Ba'al Mum on the Mizbe'ach is lashed for total Haktarah and partial Haktarah.

(Abaye): One is not lashed (more than once) for Lav shebi'Chlalos (multiple Lavim that are learned from one verse).

Zevachim 80a (Mishnah - R. Eliezer): If blood that requires four Matanos (putting it on 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)!

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

(Rava): Bal Tosif applies only at the time of the Mitzvah.

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

Answer: If another Tzibur 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 (one Matanah of a Bechor). Since if we would have another Bechor to offer, we would throw its blood, the Mitzvah applies the entire day!

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.

Rishonim

Rashba (Rosh Hashanah 16a DH Lamah): Tosfos asked why blowing extra Teki'os is not Bal Tosif. He answered that doing the same matter again is not Bal Tosif, even if he intends for the Mitzvah. I say that the Isur is only for a person to add by himself, e.g. an extra Berachah in Birkas Kohanim or to sit in a Sukah on Shemini Atzeres. Bal Tosif does not apply what Chachamim enacted. Nowadays people sleep in the Sukah on Shemini Atzeres, even though the calendar is fixed. Likewise, Bal Tigra apply when there was a need to enact, e.g. not to blow a Shofar on Rosh Hashanah that is on Shabbos.

Turei Even (16b DH v'Tok'in): Abaye asked that one who sleeps in the Sukah on Shemini Atzeres should be lashed, even though we do so due to Safek. Even though Chachamim enacted this (Sukah 47a), Bal Tosif applies! I answered this there (see below). However, Tana'im argue about Bal Tosif and Bal Tigra regarding too many or too few Matanos of blood. Each Tana gives what he holds is the best solution. If so, Bal Tosif and Bal Tigra do not apply! With difficulty, one could say that this was R. Eliezer's answer. Still, why shouldn't Bal Tosif apply to enactments of Chachamim? Why is this unlike other Mitzvos? Chachamim do not enact to uproot Mitzvos! Regarding Shofar, Chachamim may uproot the Torah through telling us to be passive. The Rashba connotes that one who neglects a Mitzvas Aseh once transgresses Bal Tigra, therefore he answered why one does not transgress for not blowing the Shofar on Shabbos. If so, according to the opinion that one is lashed for Lav she'Ein Bo Ma'aseh, one is lashed also for neglecting a Mitzvas Aseh! We never found any Tana or Amora say so.

Turei Even (28b DH Harei): One transgresses Bal Tigra only if he fulfilled the Mitzvah. E.g. if a Korban requires four Matanos on the Mizbe'ach, and he put one, he was Yotzei (b'Di'eved). However, if he did not fulfill the Mitzvah, e.g. he wore Tefilin without all four Parshiyos, or put Tzitzis on three corners, or took three of the four Minim, he did not do the Mitzvah at all, so Bal Tigra does not apply. He transgresses only the Aseh to fulfill the Mitzvah. The Gemara says that if one cannot find all four Minim, he takes what he can find, lest the Mitzvah be forgotten. We would not do so if this were Bal Tigra!

Sefas Emes (Rosh Hashanah 28b DH Ayen): The Rashba can say that one is lashed for Bal Tigra because it is Lav shebi'Chlalos. One who sleeps in a Sukah on Shemini Atzeres is lashed, i.e. mid'Rabanan. In any case, surely one who cannot do the entire Mitzvah due to Ones (he does not have all four Minim, or the blood was mixed with blood that requires only one Matanah) does not transgress.

Imrei Emes (66 DH ul'Fi): The Rashba holds that there are no lashes for Bal Tigra, just like the Rambam did not mention lashes for Bal Tosif in Hilchos Sanhedrin. Even if we do not know why, we should not argue with him. For the same reason, one is not lashed for Bal Tigra.

Ramban (Shemos 23:13): Rashi says that "uv'Chol Asher Amarti Alechem Tishameru" is a Lav for every Mitzvas Aseh. We must say that it is Lav shebi'Chlalos. If not, one would be lashed for every Aseh! All agree that one is not lashed for a Lav that includes many matters and does not mention the (particular) Aveirah. However, the Mechilta says that 'Hishamer' of an Aseh is an Aseh.

Shevet Sofer (OC 65 DH u'Mah): This answer (that Mitzvos Aseh are more stringent because also Bal Tigra applies to them) is unlike the Rambam, who says that one who rules that meat of Chayos is permitted with milk transgressed Bal Tigra. This shows that Bal Tigra applies also to Lavim! The Turei Even's question is according to the opinion that one is lashed also for Lav shebi'Chlalos. The Ramban says that all agree that one is not lashed for a Lav that includes many matters and does not mention the Aveirah. The same applies to Bal Tigra.

Sefer ha'Chinuch (454, b'Sof): One who transgresses and adds to a Mitzvah, e.g. he makes five boxes in Tefilin or puts Kosher Tefilin on his head, or takes two Lulavim in his hand or all similar matters, or he sits in a Sukah after the Chag, or he takes a Lulav with intent for the Mitzvah even though he know that the time passed, he transgressed this Mitzvah and he is lashed, with witnesses and warning, like everywhere.

Minchas Chinuch (454 DH v'Hinei ha'Rav and 455 b'Sof): The Rambam does not mention lashes for Bal Tosif. 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 Abaye discusses lashes 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 (Petichah Koleles to Shulchan Aruch, 1:37): It is difficult to say that when Abaye mentions lashes, this is mid'Rabanan

Mordechai (Sukah 772): Avi ha'Ezri (562) explains that Rava answered that lashes for Bal Tosif are only at the time of the Mitzvah, but there is an Isur even not at the time of the Mitzvah. Rava did not say that one may sleep in the Sukah then.

Poskim and Acharonim

Yom Teru'ah (28a DH Gemara): What was Abaye's question? Lashes require warning. If in Eretz Yisrael he was warned and accepted the warning, i.e. he said that he wants to transgress Bal Tosif, surely he is lashed! Rather, he discusses in Chutz la'Aretz (where we sit in the Sukah due to Safek). Abaye did not refer to real lashes, rather, an Isur Bal Tosif for which (in other cases) one is lashed.

Hilchos Ketanos (2:280,281): If one did enough to be Yotzei, but omitted parts of the Mitzvah, he transgressed Bal Tigra. If so, a Kohen who offered a Minchah and did not mix it, should be lashed! If we say that Bal Tosif and Bal Tigra are Lav shebi'Chlalos, this would answer the question.

Question: The Ramban (Shemos 20:7) asked why Aseh Docheh Lo Sa'aseh. A Lav is more stringent, for one is lashed for it! According to the Rashba, we can say that there is also a Lav (Bal Tigra) against Bitul of every Aseh. Why did the Turei Even ask that according to the Rashba, there should be lashes for Bal Tigra? It is Lav shebi'Chlalos!

Yehudah Ya'aleh (OC 173 DH u'Mah): Hilchos Ketanos was unsure about this; he did not explain why. I say that is because in we say that one who sleeps in a Sukah on Shemini Atzeres should be lashed. This shows that it is not Lav shebi'Chlalos, like the Kesef Mishneh said (Hilchos Avodah Zarah 11:1). Sefer ha'Chinuch says that one is lashed for Bal Tosif. We must say that it is like "Lo Sa'aseh Melachah" on Yom Tov, which includes all the Melachos (and it is not Lav shebi'Chlalos). In any case, we hold that one is not lashed for Lav she'Ein Bo Ma'aseh, so there are no lashes for Bal Tigra. Really, the Ramban did not ask this. The Gemara (Rashi) asked this! Even if Bal Tigra applies to Bitul of an Aseh, the Lav is more stringent, for it has lashes, but Bal Tigra does not, due to Lav shebi'Chlalos or Lav she'Ein Bo Ma'aseh.

Chasdei David (Korbanos 8 DH Chachim p.135): 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.

Beis Mordechai (2:19): Sefer ha'Chinuch does not list Birkas Kohanim among Mitzvos for which one is lashed for Bal Tosif. Perhaps he did not toil to list all of them. Or, he omitted it because Ein Bo Ma'aseh. R. Yochanan says that voice is a Ma'aseh (Temurah 3A), but Tosfos (Bava Metzi'a 90b DH Rebbi) says that this is only when the voice does a Ma'aseh. We can say that blessing the Tzibur is a Ma'aseh.

Suggestion: The Rambam exempts from lashes for Bal Tosif is because it is a Lav shebi'Chlalos. 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.