Electromagnetism, the strong interaction, and the weak interaction are mediated by spin 1 particles, and in Quantum Gravity spin 2. I saw in this question that the answers pointed out how interactions cannot be mediated by fermions but I didn't see any answers say specifically that say that mediators of interactions must specifically be spin 1 or 2, but no known interactions are mediated by gauge bosons of spin 3 or higher.

My question is, are interactions mediated by spin 3 or higher bosons allowed, and if so could they effect particles known to exist in the standard model, or could they only effect as yet undiscovered particles?