Multiple stellar populations in globular clusters (GCs) are distinct by their different abundances of light elements. The abundance anti-correlations point towards a nucleosynthesis origin due to high-temperature H burning, but it remains to be assessed which type of stars altered primordial abundances in GCs. In particular, the regime at very high temperature that shapes the variations in potassium as well as calcium and scandium, which has been detected in a few notable cases such as NGC 2419 and NGC 2808, is still poorly explored. We started a systematic search for excess of Ca (and Sc) in GC stars with respect to the level of unmodified field stars. Statistically robust evidence of such excess was found in a small number of GCs (NGC 4833, NGC 6715, NGC 6402, NGC 5296, NGC 5824, and NGC 5139/omega Centauri) that join the previously known two clusters. For the first time we show that NGC 4833 is likely to host anti-correlated K and Mg abundances. All these GCs are among the most massive ones in the Galaxy. We found that the fraction of stars with Ca enhancement at 3sigma above the field star distribution is a multivariate function of the GC mass and metallicity, as in other manifestations of the multiple population phenomenon in GCs. We argue that these alterations in only a few GCs can be reproduced by two different channels: either a class of ordinary stars, that is common to all GCs, acts only in particular environments, or an on-off mechanism is generated by the occurrence of a peculiar type of stars (or lack of such stars). Hot bottom burning in asymptotic giant branch stars in the low-metallicity regime is a good candidate for the first class. Alternatively, a metallicity dependence is also expected for supermassive stars, which are predicted to preferentially form in massive GCs. (abridged).
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