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Although there perhaps aren't too many examples, I will present here one.
If a person takes the arba minim at Sukkos (Lulav, esrog, hadasim, aravos) and adds on another min in a way they are ovar on bal tosif and they now have 5 minim, are they still yotzee the mitzvah since at the end of it all they still "took" the four minim, even though they added on another one?
OUTLINES OF HALACHOS FROM THE DAF
This is actually answered by whether or not one is required to bind the arbah minim together or can hold them together without binding them
Question: Also regarding Lulav, if one adds other species to the four, he invalidates the Mitzvah!
Answer: If Ein Tzarich Eged (the species need not be tied), holding additional species at the same time has no consequence. If Tzarich Eged, the bundle (with the extra species) was already invalid (from when he tied it.)
Rambam (Hilchos Mamrim 4:3): If a Chacham ruled to make four boxes properly, and add a fifth and stick it outside them, he is liable for Zaken Mamrei. The outermost box must see the air. He would be exempt for ruling about a Mitzvah such as Lulav or Tzitzis.
Rebuttal (Ra'avad): Also for Lulav or Tzitzis, the addition disqualifies what was there to start! Even if the Zaken Mamrei caused people to transgress Bal Tosif, he is exempt unless he disqualified the Mitzvah.
Rosh (Sukah 3:14): Bal Tosif does not apply to taking extras of the four Minim, even according to the opinion that Lulav Tzarich Eged, unless he adds a different species.
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.
In Hilkhoth Lolav 7:5, the Rambam writes as follows:
5 arba'ah minin ellu misswah ahhath hen ume`akvin zeh eth zeh wa-khulan niqra'in misswath lolav wa-ein pohhathin mehen wa-ein mosifin 'aleihen. wa-im lo nimssa ehhadh mehen ein mevi'in tahhtaw min ahher had-domeh lo.
Translation:
These four species together constitute a single misswah and the absence of any one of them prevents the misswah from being performed. And they are all together referred to as 'misswath lolav' and we do not subtract from them and we do not add. And if one of them cannot be found, we do not bring another species in its place that is similar to it.
And in the seventh halakhah there, he writes as follows:
7 kammah nottel me-hen? lolav ehhadh wa-ethrogh ehhadh ushnei baddei `aravah usheloshah baddei hadhas. wa-im rassah le-hosif ba-hadhas kedhei sheyyihyeh agudah gadholah - mosif wa-noy misswah hu. aval she'ar ham-minin ein mosifin 'al minyanam wa-ein gor'in mehen wa-im mosif o gara' - pasal.
Translation:
7 How many of each [of the four species] do we take [to perform the misswah of nettilath lolav]? One lolav and one ethrogh and two willow branches and three myrtle branches. And if one desires to add to the number of myrtle branches so that there will be a large bundle then he may add and it serves as a decoration to the misswah. But with regard to the other species, we do not add to their number and we do not subtract from them, and if one either added or subtracted he invalidates their use to fulfill the misswah.
So, essentially, if each particular species is me-`akev to the other, and if even adding or subtracting from the number of each kosher species causes the agudah to become pasulah, then kol she-ken that a fifth species added to the agudah would cause it to become pasulah and prevent from being yossei yedhei hhovatho.
Le-`aniyuth da'ati, according to the Rambam, to do so would prevent one from fulfilling the misswah of lolav. However, the Ba'alei Tosafoth on Sukkah 31b (dh"m Ho'il) state differently regarding the waving of five species:
de-le-`olam yedhei misswah yassa ella 'over 'al bal tosif
Translation:
[In doing this] a person will always fulfill the misswah [of lolav] but he will nevertheless be in violation of the prohibition of adding to a misswah.
Addendum: There are those are of the opinion that the text of the Rambam there in Hilkhoth Lolav 7:7 should be emended to read not "pasal" but "lo pasal". This is based largely on a the testimony of Rabbenu Avraham ben HaRambam who says that his father later changed his mind based on a similar argument as brought by the Ra'avadh in his hasaghoth on the Mishneh Torah. Notably, HaRav Yosef Qafihh z"l is of this opinion - which he explains in a comment (#20) which lasts for several pages - and rules that although the textual tradition for the "pasal" reading is strong and consistent, the text should nevertheless be changed to read "lo pasal" and the original reading should be viewed as stemming from a mahadhurah qamma written in the Rambam's youth.
Although the halakhah is strictly speaking of adding or detracting from the number of each of the arba`ah minim and not explicitly regarding the addition of an entirely new species in addition to the four (although 7:5 does address the exchange of kosher species for a similar non-kosher one), I believe that this is due to the fact that while it was apparently a common error to equate species with one another, to add a fifth species may not have even been a hawa mina that was prevalent enough to merit discussion.
Hope this helps. Kol tuv.
