Feasibility of many emergent phenomena that intrinsic magnetic topological insulators (TIs) may host depends crucially on our ability to engineer and efficiently tune their electronic and magnetic structures. Here we report on a large family of intrinsic magnetic TIs in the homologous series of the van der Waals compounds (MnBi₂Te₄)(Bi₂Te₃)_m with m = 0, ···, 6. Magnetic, electronic and, consequently, topological properties of these materials depend strongly on themvalue and are thus highly tunable. The antiferromagnetic (AFM) coupling between the neighboring Mn layers strongly weakens on moving from MnBi₂Te₄(m = 0) to MnBi₄Te₇ (m = 1) and MnBi₆Te₁₀ (m = 2). Further increase inmleads to change of the overall magnetic behavior to ferromagnetic (FM) one for (m = 3), while the interlayer coupling almost disappears. In this way, the AFM and FM TI states are, respectively, realized in the m = 0, 1, 2 and m = 3 cases. For largemnumbers a hitherto-unknown topologically nontrivial phase can be created, in which below the corresponding critical temperature the magnetizations of the non-interacting 2D ferromagnets, formed by the MnBi₂Te₄ building blocks, are disordered along the third direction. The variety of intrinsic magnetic TI phases in (MnBi₂Te₄)(Bi₂Te₃)_m allows efficient engineering of functional van der Waals heterostructures for topological quantum computation, as well as antiferromagnetic and 2D spintronics.