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EuCd$_2$As$_2$ is an antiferromagnetic semimetal, that can host non-trivial topological properties, depending upon its magnetic state and excitations. Here, we report the synthesis and characterization of Eu(Cd$_{1-x}$Ag$_x$)$_2$As$_2$ and Eu$_{1-y}$Na$_y$Cd$_2$As$_2$, and study the evolution and nature of magnetic order with doping. Temperature-substitution phase diagrams are constructed from the electrical resistance and magnetic susceptibility data. We observe a splitting of the magnetic transition into two different transitions, and the gradual increase in one of the transition temperatures with Ag- and Na-substitution. The other transition remains more or less independent of doping. We further show that a magnetic state with a net ferromagnetic moment is stabilized by both Ag and Na doping and this can be explained by considering the changes in band filling due to substitution as suggested by density functional theory (DFT) calculations. We thus show that chemical substitution and the subsequent changes in band filling could be a pathway to tune the magnetic ground state and to stabilize a ferromagnetic phase in EuCd$_2$As$_2$.