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I am basing this answer on the assumption that you are interested in Bal Tosef in general and not just the specific case of Lulav you gave as an example. Lulav is slightly more complicated.

There is a girsa discrepancy in the Rambam chapter seven of Lulav halacha seven if the lulav becomes passul or not by adding to it in a way that is Bal Tosef. See Raavad and Magid Mishna there, there is a discussion whether this is intrinsic to the Lulav needing to be tied (צריך אגד) or not.

The Encyclopedia Talmudis under Bal Tosef by note 76 brings opinions that a mitzvah which needs a certain amount of connected items to which an extra one is attached will in fact passul the items of proper mitzvah use. (I use this language to avoid the צריך אגד of Lulav).

This is the opinion of Tshuvas HaRashba chelek 1 siman 468 & 535(mentioned earlier in note #47), Lechem Chamudos on the Rosh hilchos Teffilin #19. The note also mentions this is the opinion of Tosafos in Succah.

However itThis idea, that he would not be yotzah, is also implied in the Minchas Chinuch that he is not Yotzeh.

See mitzvah 454 #6 he writes ומביא הרב המחבר, דמסיק רבא דלעבור על בל תוסיף בזמנו לא בעי כוונה, ושלא בזמנו בעי כוונה. והנה חמש טוטפות בתפילין אם כבר יצא ידי המצוה באותו היום הוי ליה כעבר זמנו ואינו עובר בלא כוונה וכו׳.

He seemingly takes for granted that in order to consider this person who is wearing five parshios in his Teffilin as having already fulfilled his obligation, we must give a case where he already wore a proper pair. Now, if he believed the person is yotzeh while engaged in bal yosef, he could have said this person was wearing the five parsha version without intention for kiyum mitzvah, which according to Rava would still in fact be a kiyum mitzvah as mitzvos do not need to be fulfilled consciously, after which he consciously decided to be yotzeh the mitzvah of Teffilin etc. By choosing his case, it would appear he believes the person is never yotzeh in such a situation.

There is a girsa discrepancy in the Rambam chapter seven of Lulav halacha seven if the lulav becomes passul or not by adding to it in a way that is Bal Tosef. See Raavad and Magid Mishna there, there is a discussion whether this is intrinsic to the Lulav needing to be tied (צריך אגד) or not.

The Encyclopedia Talmudis under Bal Tosef by note 76 brings opinions that a mitzvah which needs a certain amount of connected items to which an extra one is attached will in fact passul the items of proper mitzvah use. (I use this language to avoid the צריך אגד of Lulav).

This is the opinion of Tshuvas HaRashba chelek 1 siman 468 & 535(mentioned earlier in note #47), Lechem Chamudos on the Rosh hilchos Teffilin #19. The note also mentions this is the opinion of Tosafos in Succah.

However it is implied in the Minchas Chinuch that he is not Yotzeh.

See mitzvah 454 #6 he writes ומביא הרב המחבר, דמסיק רבא דלעבור על בל תוסיף בזמנו לא בעי כוונה, ושלא בזמנו בעי כוונה. והנה חמש טוטפות בתפילין אם כבר יצא ידי המצוה באותו היום הוי ליה כעבר זמנו ואינו עובר בלא כוונה וכו׳.

He seemingly takes for granted that in order to consider this person who is wearing five parshios in his Teffilin as having already fulfilled his obligation, we must give a case where he already wore a proper pair. Now, if he believed the person is yotzeh while engaged in bal yosef, he could have said this person was wearing the five parsha version without intention for kiyum mitzvah, which according to Rava would still in fact be a kiyum mitzvah as mitzvos do not need to be fulfilled consciously, after which he consciously decided to be yotzeh the mitzvah of Teffilin etc. By choosing his case, it would appear he believes the person is never yotzeh in such a situation.

I am basing this answer on the assumption that you are interested in Bal Tosef in general and not just the specific case of Lulav you gave as an example. Lulav is slightly more complicated.

There is a girsa discrepancy in the Rambam chapter seven of Lulav halacha seven if the lulav becomes passul or not by adding to it in a way that is Bal Tosef. See Raavad and Magid Mishna there, there is a discussion whether this is intrinsic to the Lulav needing to be tied (צריך אגד) or not.

The Encyclopedia Talmudis under Bal Tosef by note 76 brings opinions that a mitzvah which needs a certain amount of connected items to which an extra one is attached will in fact passul the items of proper mitzvah use. (I use this language to avoid the צריך אגד of Lulav).

This is the opinion of Tshuvas HaRashba chelek 1 siman 468 & 535(mentioned earlier in note #47), Lechem Chamudos on the Rosh hilchos Teffilin #19. The note also mentions this is the opinion of Tosafos in Succah.

This idea, that he would not be yotzah, is also implied in the Minchas Chinuch.

See mitzvah 454 #6 he writes ומביא הרב המחבר, דמסיק רבא דלעבור על בל תוסיף בזמנו לא בעי כוונה, ושלא בזמנו בעי כוונה. והנה חמש טוטפות בתפילין אם כבר יצא ידי המצוה באותו היום הוי ליה כעבר זמנו ואינו עובר בלא כוונה וכו׳.

He seemingly takes for granted that in order to consider this person who is wearing five parshios in his Teffilin as having already fulfilled his obligation, we must give a case where he already wore a proper pair. Now, if he believed the person is yotzeh while engaged in bal yosef, he could have said this person was wearing the five parsha version without intention for kiyum mitzvah, which according to Rava would still in fact be a kiyum mitzvah as mitzvos do not need to be fulfilled consciously, after which he consciously decided to be yotzeh the mitzvah of Teffilin etc. By choosing his case, it would appear he believes the person is never yotzeh in such a situation.

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There is a girsa discrepancy in the Rambam chapter seven of Lulav halacha seven if the lulav becomes passul or not by adding to it in a way that is Bal Tosef. See Raavad and Magid Mishna there, there is a discussion whether this is intrinsic to the Lulav needing to be tied (צריך אגד) or not.

The Encyclopedia Talmudis under Bal Tosef by note 76 brings opinions that a mitzvah which needs a certain amount of connected items to which an extra one is attached will in fact passul the items of proper mitzvah use. (I use this language to avoid the צריך אגד of Lulav).

This is the opinion of Tshuvas HaRashba chelek 1 siman 468 & 535(mentioned earlier in note #47), Lechem Chamudos on the Rosh hilchos Teffilin #19. The note also mentions this is the opinion of Tosafos in Succah.

However it is implied in the Minchas Chinuch that he is not Yotzeh.

See mitzvah 454 #6 he writes ומביא הרב המחבר, דמסיק רבא דלעבור על בל תוסיף בזמנו לא בעי כוונה, ושלא בזמנו בעי כוונה. והנה חמש טוטפות בתפילין אם כבר יצא ידי המצוה באותו היום הוי ליה כעבר זמנו ואינו עובר בלא כוונה וכו׳.

He seemingly takes for granted that in order to consider this person who is wearing five parshios in his Teffilin as having already fulfilled his obligation, we must give a case where he already wore a proper pair. Now, if he believed the person is yotzeh while engaged in bal yosef, he could have said this person was wearing the five parsha version without intention for kiyum mitzvah, which according to Rava would still in fact be a kiyum mitzvah as mitzvos do not need to be fulfilled consciously, after which he consciously decided to be yotzeh the mitzvah of Teffilin etc. By choosing his case, it would appear he believes the person is never yotzeh in such a situation.