Orach Chayim brings that pious men should wear both Rashi and R. Tam tefillin at once when davening (34:2-3). Do we know what the earliest halakhic sources recommending this are, and their reasoning?
The Bavli mentions somewhat ambiguously that there is space on the head for two sets (Menakhot 34), but this in itself doesn't constitute a rule or minhag.
I understand that the Tikkunei Zohar (101d) recommends both (and one answer to this question comments that "Putting on two pairs of tefillin is mostly prevalent among Hasidim and Sephardim, for Kabbalistic reasons summarized by the Lubavitcher Rebbe" -though Chabad typically wear one set after the other rather than simultaneously), but I am looking for halakhic rather than kabbalistic sources. The Chabad site's discussion on the topic does not go into historical detail.