We report on the magnitude of the intrinsic [Fe/H] spread in the Small Magellanic Cloud (SMC) intermediate-age massive clusters NGC 339, 361, Lindsay 1 and 113, respectively. In order to measure the cluster metallicity dispersions, we used accurate Stromgren photometry of carefully selected cluster red giant branch (RGB) stars. We determined the Fe-abundance spreads by employing a maximum likelihood approach. The spreads obtained using the more accurate photometry of the brighter RGB stars resulted to be marginal (∼0.05 ± 0.03 dex) for NGC 339 and NGC 361, while for Lindsay 1 and Lindsay 113, we obtained metallicity spreads of 0.00 ± 0.04 dex. From these results, we speculate that NGC 361 is added to the group of four SMC clusters with observational evidence of multiple populations (MPs). Furthermore, in the context of the present debate about the existence of Fe-abundance inhomogeneities among old clusters with MPs, these outcomes place new constrains on recent theoretical speculations for making this phenomenon visible.