Gemara

(Beraisa - R. Yosi): If one has two head Tefilin but no Shel Yad, he wraps leather around one (so it will appear like one Bayis) and ties it on his arm.

(Beraisa #1): The order of the Parshiyos - on the right are "Kadesh Li" and "Ki Yevi'acha." "Shma" and "v'Hayah Im Shamo'a" are on the left.

Contradiction: Another Beraisa (#2) gives the opposite order!

Answer (Abaye): One Beraisa gives the order for a reader (facing the wearer). The other Beraisa is with respect to the wearer.

The reader reads in order.

(Rav Chananel): If the order was changed, they are Pesulim.

(Abaye): This is only if a Parshah that should be on the outside (extreme left or right) is on the inside, but if the outside Parshiyos were switched (with each other), or the inside ones were switched, it is Kosher.

Objection (Rava): Surely, if an outside Parshah was switched with an inside one, it is Pasul, for the Parshah must be 'exposed'. Likewise, when the outside Parshiyos are switched with each other, the Parshah that should be 'exposed' to the right is not! Rather, in either case it is Pasul.

Eruvin 95a (Mishnah): If one finds Tefilin (on Shabbos in a field, where they are prone to be disgraced) he brings them in one pair at a time;

R. Gamliel says, he brings two pairs at a time.

95b: Rav Shmuel taught that there is room on the head to wear two Tefilin at a time. The same applies to the arm.

The Tana'im argue about Rav Shmuel's law. Alternatively, all agree to his law. They argue about whether the Mitzvah applies on Shabbos. Alternatively, they argue about whether Mitzvos require intent, or whether intent is required to transgress Bal Tosif (adding to Mitzvos).

96a: Do not say that all agree that there is no Mitzvah on Shabbos, and they argue about whether Bal Tosif requires intent when the Mitzvah does not apply. Rather, we must answer like above.

Rishonim

Rif and Rosh (Hilchos Tefilin (after Menachos) 7a and Siman 6): Abaye said that if the outside Parshiyos were switched, or the inside ones were switched, it is Kosher. The Halachah does not follow him.

Rambam (Hilchos Tefilin 3:5): In the head Tefilin, the last Parshah, v'Hayah Im Shamo'a, is in the box on the right of the wearer. Shma is next to it, then Ki Yevi'acha, and Kadesh Li is in the fourth box, on the left. One who faces the wearer reads in this order (Kadesh Li, Ki Yevi'acha, Shma and v'Hayah Im Shamo'a, from right to left). If he switched the order, they are Pesulim.

Migdal Oz: Shamayim showed that there is an argument above (about the proper order) just like the argument here below. One who understands the Sod that Hash-m wears Tefilin will know that both opinions are Divrei Elokim Chayim. We found a hidden Medrash that forced us to change our custom.

Aruch ha'Shulchan (OC 34:6-9): Rashi or R. Tam Tefilin are Pasul. How can it be that Ge'onei Olam and Kelal Yisrael did not fulfill Tefilin and blessed Levatalah?! Migdal Oz means that they used to do like R. Tam, and they switched to Rashi. The hidden Medrash is the Zohar in Pinchas. It says that the Parshiyos are in order. Some reject this and say that in time, they are written in order, but they are not placed in the boxes in order. The Zohar says that in the future, there will be no Yetzer ha'Ra or punishments, so Shma (which has only Ahavas Hash-m) will be last, like R. Tam.

Rosh (5): Rashi explains that the reader reads in the order the Parshiyos appear in the Torah, i.e. Kadesh Li, Ki Yevi'acha, Shma and v'Hayah Im Shamo'a. R. Tam explains that Kadesh Li and Ki Yevi'acha are to the right of the reader, and Shma and v'Hayah Im Shamo'a are to the left of the reader, with Shma on the outside. R. Chananel, Rav Hai Gaon, Rav Shrirah Gaon, and Teshuvas ha'Ge'onim of R. Yosef Tuv Elem say similarly. Shimusha Raba (a Ga'on's compilation of Hilchos Tefilin; the Rosh brings it after Siman 31) is like Rashi. The Mechilta connotes like Rashi. Since the greatest sages argue about this, and only one is Kosher, and there is room on the head for two Tefilin, and also on the arm, one with Yir'as Shamayim will make one pair of Tefilin according to each opinion, and wear both together. He intends to be Yotzei with the Kosher pair; the other pair is merely straps. Bal Tosif is only if one makes five boxes. One may not put both pairs in one bag, for Chulin should not be in a bag for Kodesh. Rather, he makes a bag for each and labels it (so each pair is always in its bag).

Ma'adanei Yom Tov (20): The Halachah follows Chachamim; we conclude that they forbid more than one pair due to Bal Tosif. Do not say that we conclude that they argue about whether there is room to wear two Tefilin at once, and Chachamim say no, for the Rosh rules that there is room!

Poskim

Shulchan Aruch (OC 34:1): The universal custom is like Rashi and the Rambam.

Mishnah Berurah (4): The Beis Yosef, Gra and Acharonim conclude that Rashi's opinion is primary.

Shulchan Aruch (2): One with Yir'as Shamayim will fulfill both opinions. He makes two pairs of Tefilin and wears both. He intends to be Yotzei with the Kosher pair; the other pair is merely straps.

Taz (2 DH Nish'alti): One who wears both pairs at once must wear Rashi below, closer to the primary place of Tefilin (near the face, and near the elbow), for it is not clear that there is room for both.

Shulchan Aruch (ibid): There is room on the head for two Tefilin, and also on the arm. If he cannot gauge the proper place for both, he puts one on the hand and head, and removes them and immediately puts on the other, relying on his first Berachah. Some say that if he can wear only one, he blesses on Rashi Tefilin, and wears them at the time of Keri'as Shma and Tefilah. After Tefilah he puts on R. Tam Tefilin and reads "Shma", and then "v'Hayah Im Shamo'a."

Beis Yosef (DH u'Mah she'Chosav Rabeinu b'Shem): Semag and Sefer ha'Terumos say that if he cannot gauge the proper place for both, he puts one on the hand and head, and removes them and immediately puts on the other, relying on his first Berachah. Even though the Berachah on the head Tefilin interrupts between one hand Tefilin and the other, this is better than putting them on without any Berachah. Some say that if he can wear only one, he wears Rashi Tefilin, blesses on them and wears them at the time of Keri'as Shma and Tefilah. After Tefilah he puts on R. Tam Tefilin and reads "Shma", and then "v'Hayah Im Shamo'a."

Shulchan Aruch (3): One should do so only if he is established and known for Chasidus (doing more than the Halachah requires).

Maharil 137 (brought in Beis Yosef DH u'Motzasi): I did not find old Rabanan doing so. We do like our predecessors. We rely on Semag, who says that old Tefilin were found near Yechezkeil's grave, like Rashi.

Drishah [1]: My Rebbi said that this does not refute R. Tam. He can explain that they were put in Genuizah (buried) because they were Pasul, i.e. they were written out of order! We bury Pasul Seforim in the graves of Tzadikim!

Rejection (Bach 1, b'Sof): This is wrong. This would not obligate burying them. One can switch the order of the Parshiyos!

Teshuvas R. Akiva Eiger (2:8): If one found head Tefilin arranged like R. Tam's opinion, he may re-order them like Rashi. We do not consider them like Tefilin written Lo Lishmah. It suffices to write with intent for Kedushas Tefilin. One need not intend for Rashi or R. Tam Tefilin. The Bach holds that if the Halachah followed R. Tam, one could convert Rashi Tefilin to R. Tam Tefilin. Likewise, we hold that one can convert R. Tam Tefilin to Rashi Tefilin! However, the Bach's rejection is obvious. Why didn't the Drishah anticipate this? It seems that the Drishah argues, and holds that one cannot convert them, for it is as if they were written Lo Lishmah. Rather than make a new argument, I prefer to say that Rashi holds that Parshas v'Hayah (Im Shamo'a) must conclude with "Al ha'Aretz" at the end of the line. Rashi and R. Tam agree that Shma begins at the beginning of the line. If we will switch the order to R. Tam and put v'Hayah before Shma, there will not be any space in between before Parshas Shma. (It should have nine spaxces before it, for it is open.) The Magen Avraham (148) says in the name of Semak that we are not concerned for open or closed Parshiyos in the head Tefilin, which are separate parchments, but the custom is to be particular about this. Perhaps R. Tam argues with Semak, and holds that one must be particular also for the head Tefilin. This is why the Drishah said 'this does not refute R. Tam'; he did not totally reject the proof. Semag (and Mordechai, who also brought this proof) hold like Semak.

Note: The Drishah said 'Adarabah' (just the contrary), which connotes that the Tefilin found supports R. Tam's opinion.

R. Akiva Eiger (ibid.): The Bach holds that since we hold like Semak, R. Tam is refuted. Alternatively, perhaps they found only hand Tefilin, in which we cannot switch the order of the Parshiyos, for they are on one parchment. Still, one could cut them apart and put them in one Bayis. The Drishah holds that R. Tam can say that they were buried because they were written according to Rashi's order. The Beis Yosef says that one must sew or glue them together, so there will be no space before Parshas Shma, like I said above.

R. Akiva Eiger (ibid.): However, perhaps one cannot change the order. We have a Safek. Perhaps R. Tam's order is primary. If so, to re-arrange them like Rashi Tefilin lowers their Kedushah! However, since our custom is like Rashi, and we do not wear R. Tam Tefilin, and we are not concerned for a Safek mid'Oraisa (t` we do not fulfill the Mitzvah, or for Berachah l'Vatalah), this shows that Rashi's opinion is primary, and this does not lower the Kedushah. If so, one may put Rashi Tefilin in a bag designated for R. Tam Tefilin, unless he is stringent to wear also R. Tam Tefilin. Only such a person must be concerned for lowering the Kedushah.

Maharil (ibid.) Also R. Tam (Hagahos Tur ha'Shalem 4, citing the Chida - this is not the grandson of Rashi who concluded that Shma is on the outside. It is a different Rishon called R. Tam) asked in a dream about this. Since the custom is not to be stringent, it is haughtiness to be stringent, unless he is known for Chasidus. The ones I saw wearing both do not fulfill this. One who wears both should wear them together. If he cannot, he blesses on Rashi Tefilin, for the custom is like him. R. Tam Tefilin is only to fulfill all opinions. Similarly, on Pesach we bless only on Matzah, and then eat Matzah with Maror without a Berachah, like Hillel. Whoever reads the Megilah on the 14th and 15th (due to a Safek if the city was walled from the days of Yehoshua) blesses only on the 14th, like most places. One should wear Rashi Tefilin at the time of Keri'as Shma and Tefilah; since most hold like Rashi, one should not separate from the Tzibur to make factions. After Davening, he puts on R. Tam Tefilin. If he is concerned for testifying against himself, he will read Shma and v'Hayah Im Shamo'a while wearing them.

Ben Ish Chai (1 Yayera 21): The Ari Zal received from Eliyahu that both are Emes. One must make both. From Moshe Rabbeinu until the Ge'onim, they wore two pairs. One must wear them together.

Halichos Olam (Vayera 5): It would be ideal to wear Rashi and R. Tam Tefilin together, but concern lest they be in the wrong place overrides this. Nowadays, R. Tam Tefilin are not only for Yir'ei Shamayim! The Shulchan Aruch and some Mekubalim are unsure which is Kosher. One should intend that the other is mere straps, lest he transgress Bal Tosif.

Ohr l'Tziyon (2:3:8): One should stipulate once 'if the Kabalah is correct, I wear both l'Shem Mitzvah. If not, I wear l'Shem Mitzvah the pair that is like the Halachah, and the other is mere straps.'