At Which Point in Davening Should the Rabbeinu Tam be Put On?
Violating Ba’al Tigra with an Extra Pair of Tefillin
Who should wear Rabbeinu Tam tefillin?
The Mechaber writes that "scrupulous people should fulfill both opinions and wear both types of tefillin, but only someone who is renowned in piety." Someone who is stringent in other areas can wear extra tefillin without being seen as a showoff. The Acharonim note that today, when many people wear Rabbeinu Tam tefillin, it would not seem arrogant for an individual to wear them and it is even praiseworthy for someone do so. According to the Gra, however, it is not necessary to ever wear Rabbeinu Tam tefillin because the halacha follows Rashi and if a person wishes to wear them in an effort to fulfill all opinions, he would have to don as many as 36 other pairs in order to fulfill the many opinions of the Rishonim. Nonetheless, there is an opinion that everyone should wear Rabbeinu Tam tefillin once in his life so that he should not be considered "a body that has not donned tefillin" (see Rosh Hashana 17a).
(סעיף ב-ג וס"ק יז; ביאורים ומוספים דרשו, 24)
At which point in davening should the Rabbeinu Tam be donned?
Those who wear both types of tefillin separately should wear Rashi’s tefillin during davening and Rabbeinu Tam’s after davening (without a beracha), and many are careful to do it this way. Those who don Rabbeinu Tam tefillin during chazaras hashatz are acting incorrectly by removing Rashi’s tefillin before UvaL’tzion and by potentially interrupting between the shel yad and shel rosh by responding amen to a beracha of chazaras hashatz. In addition, by putting on tefillin one is distracted from listening to chazaras hashatz. Someone whose time is limited may be permitted to don them during chazaras hashatz if he has no other time to put them on.
(סעיף ב וס"ק ה ו־יד; ביאורים ומוספים דרשו, 19)
Violating ba’al tigra with an extra pair of tefillin
We have learned that someone who wears both Rashi and Rabbeinu Tam tefillin must bear in mind to fulfill the obligation with only the true tefillin and view the other pair as non-mitzva. There is, in addition to the previous reason of ba’al tosif, a second reason to have this intention: ba’al tigra (the prohibition of omitting a mitzva). In the shel rosh of either pair, the first two parshios are in order and the other two are subject to a machlokes and are invalid according to one opinion. If the wearer has in mind to unconditionally fulfill the mitzva with the pair he is currently wearing, he will violate ba’al tigra according to the opinion which disqualifies that arrangement. (Although according to Kabbalah both arrangements are correct, the poskim disagree and the halacha follows the poskim.)
(ס"ק יג וביה"ל ד"ה יניח)
It is forbidden to add mitzvos to the Torah, as it says: "You shall preserve all I have commanded you; do not add to it."
One method of violating ba’al tosif is to add a component to a mitzva object. Examples include adding an extra species to the four minim of Sukkos or an extra string to the tzitzis.
It is forbidden mid’oraisa to wear two pairs of tefillin at the same time or to place two sets of parshios (Rashi and Rabbeinu Tam) in one bayis.
Exchanging the components of Rashi tefillin and Rabbeinu Tam tefillin