  In our HST photometric survey, we have been searching for multiple stellar
populations (MPs) in Magellanic Clouds (MCs) massive star clusters which span a
significant range of ages ($\sim 1.5-11$ Gyr). In the previous papers of the
series, we have shown that the age of the cluster represents one of the key
factors in shaping the origin of the chemical anomalies. Here we present the
analysis of four additional clusters in the MCs, namely Lindsay 38, Lindsay
113, NGC 2121 and NGC 2155, for which we recently obtained new UV HST
observations. These clusters are more massive than $\sim 10^4M_{\odot}$ and
have ages between $\sim 2.5-6$ Gyr, i.e. located in a previously unexplored
region of the cluster age/mass diagram. We found chemical anomalies, in the
form of N spreads, in three out of four clusters in the sample, namely in NGC
2121, NGC 2155 and Lindsay 113. By combining data from our survey and HST
photometry for 3 additional clusters in the Milky Way (namely 47 Tuc, M15 and
NGC 2419), we show that the extent of the MPs in the form of N spread is a
strong function of age, with older clusters having larger N spreads with
respect to the younger ones. Hence, we confirm that cluster age plays a
significant role in the onset of MPs.
