A situation arises when non-Kohanim need to be honored with first Aliyah, such as at a family celebration. Although the Kohen has the first right to the Aliyah, it is acceptable for him to forego this honor so that others may be called up to the Torah. The Rama (Orah Haim 135:1) says that a solution is to simply add supplementary Aliyot, such that the Kohen and the honorees may go up. Rabbi Yosef Benaim (Noheg BeHochma, pg.144) and Rabbi Moshe Toledano (HaShamaim Hadashim § 282) write that the Moroccan custom, however, is not to add Aliyot on the readings of Monday, Thursday or Shabbat Minha, but rather to ask the Kohen to temporarily step out of the sanctuary while the non-Kohanimare called up. This is not the case on Shabbat or the holidays, when it is common to add Mosifim, supplementary Aliyot. The HIDA (LeDavid Emet ch. 5) writes that one need not even ask the Kohen to step out, and that as long as he forwent his honor, he may stay in the sanctuary.
Summary: If necessary, a Kohen may be asked to temporarily leave the sanctuary so that a non-Kohen may get a first Aliyah when the Torah is read on Monday, Thursday or Shabbat Minha.