We investigated the magnetic properties of antiferromagnetic (AFM) topological insulator MnBi$_2$Te$_4$ with partial substitution of Mn atoms by non-magnetic elements (A$_x^{IV}$ = Ge, Pb, Sn). Samples with various element concentrations (10-80%) were studied using SQUID magnetometry. The results demonstrate that, for all substitutes the type of magnetic ordering remains AFM, while the Nèel temperature (T$_N$) and spin-flop transition field (H$_{SF}$) decrease with increasing A$_x^{IV}$ = Ge, Pb, Sn concentration. The rate of decrease varies among the elements, being highest for Pb, followed by Sn and Ge. This behavior is attributed to combined effects of magnetic dilution and lattice parameter increase on magnetic properties, most prominent in (Mn$_{1−x}$Pb$_x$)Bi$_2$Te$_4$. Besides this, the linear approximation of experimental data of T$_N$ and H$_{SF}$ suggests higher magnetic parameters for pure MnBi$_2$Te$_4$ than observed experimentally, indicating the possibility of their non-monotonic variation at low concentrations and the potential for enhancing magnetic properties through doping MnBi$_2$Te$_4$ with small amounts of nonmagnetic impurities. Notably, the (Mn$_{1−x}$Pb$_x$)Bi$_2$Te$_4$ sample with 10% Pb substitution indeed exhibits increased magnetic parameters, which is also validated by local analyses using ARPES. Our findings shed light on tailoring the magnetic behavior of MnBi$_2$Te$_4$-based materials, offering insights for potential applications in device technologies.