  Using angle-resolved photoemission spectroscopy (ARPES) and density
functional theory (DFT), an experimental and theoretical study of changes in
the electronic structure (dispersion dependencies) and corresponding
modification of the energy band gap at the Dirac point (DP) for topological
insulator (TI) $\mathrm{Mn}_{1-x} \mathrm{Ge}_x \mathrm{Bi}_2 \mathrm{Te}_4$
have been carried out with gradual replacement of magnetic Mn atoms by
non-magnetic Ge atoms when concentration of the latter was varied from 10$\%$
to 75$\%$. It was shown that when Ge concentration increases then the bulk band
gap decreases and reaches zero plateau in the concentration range of
45$\%$-60$\%$ while non-topological surface states (TSS) are present and
exhibit an energy splitting of 100 and 70 meV in different types of
measurements. It was also shown that TSS disappear from the measured band
dispersions at a Ge concentration of about 40$\%$. DFT calculations of
$\mathrm{Mn}_{1-x} \mathrm{Ge}_x \mathrm{Bi}_2 \mathrm{Te}_4$ band structure
were carried out to identify the nature of observed band dispersion features
and to analyze a possibility of magnetic Weyl semimetal state formation in this
system. These calculations were performed for both antiferromagnetic (AFM) and
ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength
was varied or a strain (compression or tension) along the $c$-axis was applied.
Calculations show that two different series of topological phase transitions
(TPTs) may be implemented in this system depending on the magnetic ordering. At
AFM ordering transition between TI and trivial insulator phase goes through the
Dirac semimetal state, whereas for FM phase such route admits three
intermediate states instead of one (TI - Dirac semimetal - Weyl semimetal -
Dirac semimetal - trivial insulator).
