The previous Halacha mentioned that although the custom in Morocco was not to wear Tefilin of Rabbenu Tam because of the appearance of haughtiness, there are opinions that this is no longer concern. The Shulhan Aruch (O.H. 34:2) records three opinions of how the Tefilin of Rabbenu Tam should be placed vis-a-vis Tefilin of Rashi. The first approach is that both types of Tefilin are donned simultaneously, but as mentioned in a previous Halacha, there is an opinion that only the area of the biceps closer to the elbow is valid, and thus it may be difficult to place both Tefiln Shel Yad. The next option is that one type of Tefilin is placed with a blessing, and then immediately removed so that second type can be placed, and the Shulhan Aruch does not mention which comes first. The third opinion and that which is most commonly practiced, is that Tefilin of Rashi are placed first with a blessing and are left on for the duration of the prayer. After the Amida, they are removed and Tefilin of Rabbenu Tam are placed without a blessing.
Rabbi Kalifa ben Malka (Kaf Naki, Hilchot Tefilin) of Agadir, Morocco cites Rabbi Yitzhak Nahon of Tetouan, who says that it is preferable to place one type of Tefilin after the other, and there is no concern of appearing overly-religious, since they are placed in sequence and not simultaneously. On the other hand, according to the Mekubalim, each type of Tefilin has its unique significance and intention, and thus should specifically be donned at the same time. Indeed, the Ben Ish Hai, following the opinion of the Vilna Gaon, says that the entire length of the biceps muscle is valid. Nevertheless, this goes against the opinion of the Shulhan Aruch which only permits the half closer to the elbow, and practically speaking, fitting both types of Tefilin is unrealistic in most instances . Accordingly, Rabbi Ben Zion Abba Shaul (Or Lezion, vol. II) and Rabbi Ovadia Yosef (Yabia Omer, vol. I, § 4) both say that if there is not enough room on the biceps, the Tefilin of Rabbenu Tam should be placed after the Tefilin of Rashi are removed.
Interestingly, Rabbi Kalifa ben Malka writes (and even summarized his words in a poem) about three other types of Tefilin in addition to Rashi and Rabbenu Tam, namely the Shimusha Raba, the Arizal and the Raavad. Since there are multiple types he offers a novel way to fulfil all opinions: Rashi Tefilin should be donned daily; the Tefilin of the Arizal should be placed on public fasts; the Shimusha Raba should be worn on Rosh Hodesh; Raavad during Aseret Yeme Teshuva; and the Tefilin of Rabbenu Tam should be placed on the day following Yom Kippur. He mentions that after Yom Kippur one is purified from any sins and one is considered to be a Hasid, a pious person. Since one is given this status of being pious, one can take that opportunity and place the Tefilin of Rabbenu Tam without the concern of appearing overly-religious or haughty. Although no one follows this stringency, it demonstrates the meticulousness with which our Hachamim were about keeping the Mitzvot.
Summary: If one has the practice of wearing Rabben Tam Tefilin, they should be donned after the Amida, once the Rashi Tefilin are removed. No blessing is recited when the Rabbenu Tam Tefilin are placed.