The search for new direct bandgap, earth-abundant semiconductors for efficient, high-quality optoelectronic devices, as well as photovoltaic and photocatalytic energy conversion has attracted considerable interest. One methodology for the search is to study ternary and multiternary semiconductors with more elements and more flexible properties. Cation mutation such as binary → ternary → quaternary for ZnS → CuGaS₂ → Cu₂ZnSnS₄ and ZnO → LiGaO₂ → Li₂ZnGeO₄ led to a series of new quaternary chalcogenide and oxide semiconductors with wide applications. Similarly, starting with GaN, ternary nitrides such as ZnSnN₂ and ZnGeN₂ have been designed and synthesized recently. However, quaternary nitride semiconductors have never been reported either theoretically or experimentally. Through a combination of the Materials Genome database with the first-principles calculations, we designed a series of quaternary nitride compounds I–III–Ge₂N₄ (I = Cu, Ag, Li, Na, K; III = Al, Ga, In) following the GaN → ZnGeN₂ → I–III–Ge₂N₄mutation. Akin to Li₂ZnGeO₄, these quaternary nitrides crystallize in a wurtzite-derived structure as their ground state. The thermodynamic stability analysis shows that while most of them are not stable with respect to phase separation, there are two key exceptions (i.e., LiAlGe₂N₄ and LiGaGe₂N₄), which are stable and can be synthesized without any secondary phases. Interestingly, they are both lattice-matched to GaN and ZnO, and their band gaps are direct and larger than that of GaN, 4.36 and 3.74 eV, respectively. They have valence band edges as low as ZnO and conduction band edges as high as GaN, thereby combining the best of GaN and ZnO in a single material. We predict that flexible and efficient band structure engineering can be achieved through forming GaN/LiAlGe₂N₄/LiGaGe₂N₄ heterostructures, which have tremendous potential for ultraviolet optoelectronics.