Did the Leviim stand on Mount Gerizim, or between the two mountains--in Shechem--or some of both? (Compare the linked chumash with "The area between the two mountains is enclosed, the Ark is situated in the middle, the priests and Levites surround the Ark and all of Israel stands on either side," from here.)
The Art Scroll Chumash explains that the bulk of the tribe of Levi stood on Har Grizim, while the elders of the tribe, the Kohanim, and the Ark were in the valley between.
Six tribes would stand on one mountain and six tribes on the other, with the Ark, the Kohanim, and the elders of the Levites in between.
Note that Rashi is a bit unclear as he has the Levites both on the mountain and in the middle. I will clarify this after I give the exact quote from Rashi.
to bless the people: As it is found in Tractate Sotah (32a): Six tribes ascended to the top of Mount Gerizim and [the other] six to the top of Mount Ebal; the kohanim , the Levites and the [holy] ark stood below in the middle. The Levites turned their faces towards Mount Gerizim and began with the blessing: “Blessed be the man who does not make a graven or molten image…,” and these [the tribes on Mount Gerizim] and these [the tribes on Mount Ebal] answered “Amen!” Then [the Levites] turned their faces towards Mount Ebal and began with the curse, saying: “Cursed be the man who makes any graven [or molten] image…,” and these [the tribes on Mount Gerizim] and these [the tribes on Mount Ebal] responded “Amen!” The Levites then turned their faces once again towards Mount Gerizim, and said: “Blessed be he who does not degrade his father and mother,” [and the tribes on Mount Gerizim and those on Mount Ebal responded “Amen!” The Levites] would then turn their faces once again towards Mount Ebal, and say: “Cursed be he who degrades his father and mother,” [and the tribes on Mount Gerizim and those on Mount Ebal responded “Amen!”]. Thus [it would continue] in this manner for all of them [the blessings and curses] until [the very last curse, namely (verse 26)]:“Cursed be the one who does not uphold [the words of this Torah].”
Oznaim LaTorah explains that there are always twelve tribes, so that Yosef is referred to as one tribe. The bulk of Levi were on the mountain because they needed to be blessed just as much as the rest of Bnai Yisrael.
Rav Hirsch explains in verse 14
וענו הלוים: The bulk of the Levites stood with the other tribes at Gerisim (V.12). In the middle between the two mounts only the זקני כהונה ולויה, the elders of the priesthood and the Levites stood, or only כל הראוי לשרת, those called on for service in the Sanctuary between the ages of thirty and fifty (Sota 37a and Numb. IV; see Josh. VIII,23).