  In de Rham-Gabadadze-Tolley (dRGT) massive gravity and bigravity, a
non-minimal matter coupling involving both metrics generically re-introduces
the Boulware--Deser (BD) ghost. A non-minimal matter coupling via a simple, yet
specific composite metric has been proposed, which eliminates the BD ghost
below the strong coupling scale. Working explicitly in the metric formulation
and for arbitrary spacetime dimensions, we show that this composite metric is
the unique consistent non-minimal matter coupling below the strong coupling
scale, which emerges out of two diagnostics, namely, absence of Ostrogradski
ghosts in the decoupling limit and absence of the BD ghost from matter quantum
loop corrections.
