  If not properly accounted for, unresolved binary stars can induce a bias in
the photometric determination of star cluster masses inferred from star counts
and the luminosity function. A correction factor close to 1.15 (for a binary
fraction of 0.35) was found in \citep{Boro19}, which needs to be applied to
blind photometric mass estimates. This value for the correction factor was
found to be smaller than literature values. In an attempt to lift this
discrepancy, in this work the focus is on higher order multiple stars with the
goal of investigating the effect of triple and quadruple systems adopting the
same methodology and data-set as in the quoted work. Then the result is found
that when triple and quadruple together with binary systems are properly
accounted for, the actual cluster mass (computed as all stars were single)
should be incremented by a factor of 1.18$-$1.27, depending on the cluster and
when the binary fraction $\alpha$ is 0.35. Fitting formulae are provided to
derive the increment factor for different binary star percentages.
