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 the m value 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 in m leads 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 large m numbers 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.