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Recent Gaia photometry of the open cluster M37 have disclosed the existence of an extended main-sequence turn off -- like in Magellanic clusters younger than about 2 Gyr -- and a main sequence that is broadened in colour beyond what is expected from the photometric errors, at magnitudes well below the region of the extended turn off, where neither age differences nor rotation rates (the candidates to explain the extended turn off phenomenon) are expected to play a role. Moreover, not even the contribution of unresolved binaries can fully explain the observed broadening. We investigated the reasons behind this broadening by making use of synthetic stellar populations and differential colour-colour diagrams using a combination of Gaia and Sloan filters. From our analysis we have concluded that the observed colour spread in the Gaia colour-magnitude diagram can be reproduced by a combination of either a metallicity spread Delta[Fe/H] ~ 0.15 plus a differential reddening across the face of the cluster spanning a total range DeltaE (B - V) ~ 0.06, or a spread of the initial helium mass fraction DeltaY ~ 0.10 plus a smaller range of reddening DeltaE (B - V) ~ 0.03. High-resolution differential abundance determinations of a sizeable sample of cluster stars are necessary to confirm or exclude the presence of a metal abundance spread. Our results raise the possibility that also individual open clusters, like globular clusters and massive star clusters, host stars born with different initial chemical compositions.