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We reconsider the possibility of a class of new kinetic terms in the firstorder (vielbein) formulation of massive gravity and multi-gravity. We find thatnew degrees of freedom emerge which are not associated with the Boulware--Deserghost and are intrinsic to the vielbein formulation. These new degrees offreedom are associated with the Lorentz transformations which encode theadditional variables contained in the vielbein over the metric. Although theyare not guaranteed to be ghostly, they are nevertheless infinitely stronglycoupled on Minkowski spacetime and are not part of the spin-2 multiplet. Hencetheir existence implies the uniqueness of the Einstein--Hilbert term as thekinetic term for a massive graviton.

New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in Vielbein Form