Any ghost-free spin-2 or spin-3 TDiff model is equivalent, via source and field redefinitions, to the Maxwell-like model, which matches the string tensionless doublet action.
Higher Spin Field Theory, Vol 1+2,
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Equivalence of spin-2 and spin-3 models invariant under transverse diffeomorphisms and the tensionless limit of string theory
Any ghost-free spin-2 or spin-3 TDiff model is equivalent, via source and field redefinitions, to the Maxwell-like model, which matches the string tensionless doublet action.