We demonstrate that Zn(Mg)O:Ga layers can be grown by molecular beam epitaxy in a two-dimensional mode with high structural perfection up to Ga mole fractions of about 6.5%. The doping efficiency is practically 100% so that free-carrier concentrations of almost 1021 cm−3 can be realized providing a zero-crossover wavelength of the real part of the dielectric function as short as 1.36 μm, while the plasmonic damping does not exceed 50 meV. Structural, electrical, and optical data consistently demonstrate a profound change of the Ga incorporation mode beyond concentrations of 1021 cm−3 attended by deterioration of the plasmonic features.