At certain compositions Ni-Mn-$X$ Heusler alloys ($X$: group IIIA-VA elements) undergo martensitic transformations, and many of them exhibit inverse magnetocaloric effects. In alloys where $X$ is Sn, the isothermal entropy change is largest among the Heusler alloys, particularly in Ni$_{50}$Mn$_{37}$Sn$_{13}$ where it reaches a value of 20 Jkg$^{-1}$K$^{-1}$ for a field of 5T. We substitute Ni with Fe and Co in this alloy, each in amounts of 1 at% and 3 at% to perturb the electronic concentration and examine the resulting changes in the magnetocaloric properties. Increasing both Fe and Co concentrations causes the martensitic transition temperature to decrease, whereby the substitution by Co at both compositions or substituting 1 at% Fe leads to a decrease in the magnetocaloric effect. On the other hand, the magnetocaloric effect in the alloy with 3 at% Fe leads to an increase in the value of the entropy change to about 30 Jkg$^{-1}$K$^{-1}$ at 5T.