As an ideal platform for studying interplays between symmetry, topology, and magnetism, the magnetic topological insulator (MTI) $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ has attracted extensive attention. However, its strong $n$-type intrinsic defects hinder the realizations of exotic phenomena. Stimulated by recent discoveries that Ge doping can efficiently tune the position of Fermi level, here we systematically investigate the band evolution and topological phase diagram with doping concentration from MTI $\mathrm{MnB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$ to strong topological insulator $\mathrm{GeB}{\mathrm{i}}_2\mathrm{T}{\mathrm{e}}_4$. Different from magnetically doped $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{e}}_3$, the topology here is determined by the competition of two band inversions arising from band folding of two time-reversal invariant momenta between antiferromagnetic and nonmagnetic/ferromagnetic unit cells. By employing a band momentum mapping method based on the first-principles calculations, besides the known MTI phase, remarkably, we find two classes of magnetic Dirac semimetal phases at antiferromagnetic state, two classes of Weyl semimetal phases at the ferromagnetic state and an intermediate trivial state at different doping regions. Interestingly, the trivial state can be tuned into a Weyl phase with two coexisting band inversions and extraordinarily long Fermi arcs by a small strain. Our work reveals diverse topological states with intrinsic quantum phenomena can be achieved with great potential for designing future electronic devices.

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• First-principles calculations
• Symmetry protected topological states
• Topological insulators
• Topological materials
• Topological phase transition