May the two pairs of tefillin (Rashi and Rabbeinu Tam) be stored in the same pouch?

Synopsis

The Mechaber rules that the two pairs may not be stored in the same pouch, since one pair is considered chol (non-sacred) relative to the other, and it is forbidden to place a chol item in a tefillin pouch. Each pair must have its own dedicated pouch with a distinguishing mark.

Early Acharonim
Late Acharonim
Lenient
Strict
Lesser cited
Major authority

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