Can you get prion diseases by eating anything other than brains?

Possiby organ meats: Prions travel through the immune system and may be found in the spleen. Any organ that accumulates prions can be the source of an infection.

Yes: Infectious types of prions have even been found in muscle tissue. But it's not that they could concentrate there adequately to cause infection. The entire biosphere has a substratum of prions with which all biological systems are in equilibrium. For infection to occur, this equilibrium must be tipped adversely which is hard to do. Feeding prion infected beef back to cattle can do, or cannibalism.