Classical double copy and higher-spin fields

Kerr-Schild double copy is shown to extend naturally to all free symmetric gauge fields propagating on $(A)dS$ in any dimension. Similarly to the standard lower-spin case, the higher-spin multicopy comes along with the zeroth, single, and double copies. The mass-like term of the Fronsdal spin $s$ field equations fixed by gauge symmetry and the mass of the zeroth copy both appear to be remarkably fine-tuned to fit the multicopy pattern forming a spectrum organized by higher-spin symmetry. On the black hole side this curious observation fills up the list of miraculous properties of the Kerr solution.