Nitrogen-rich compounds have attracted significant fundamental and practical interest owing to their ability to accommodate diverse nitrogen-bonding patterns and their feasibility as high-energy-density materials. Herein, we examine a wide range of chemical compositions in the compressed Ga-N system using first-principles structural search and experimental preparation using a laser-heated diamond anvil cell. Our investigations have theoretically identified three thermodynamically stable stoichiometries─GaN15, GaN10, and GaN5─with surprisingly versatile polymeric nitrogen framework topologies. Strikingly, our results show that the required synthetic pressures for forming polymeric nitrogen phases in GaN10 and GaN5 are much lower than that for pure solid nitrogen. Finally, we evaluated the energy involved in decomposing the compounds and validated that they are promising candidates for high-energy-density materials. These findings have broad implications for designing and synthesizing novel nitrogen-rich compounds through the reaction between p electron elements and nitrogen at modest pressures and for nitrogen chemistry under extreme conditions.