Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks: SE(3) invariance in pose estimation, permutation symmetry among agents, and scaling symmetry in dynamics. Existing methods typically exploit one symmetry at a time, leaving cross-space interactions unmodeled and wasting the combined representational power of multiple symmetries. This paper formalizes cross-space symmetry compositions as group products acting on heterogeneous state and action spaces. The authors derive equivariant network architectures that respect these composed symmetries without manual feature engineering. They prove that such networks generalize better across variations in robot morphology, task geometry, and environmental configuration than networks encoding only a single symmetry group. Empirical evaluation on a suite of manipulation and locomotion benchmarks demonstrates consistent improvements over single-symmetry baselines. Notably, the composed-symmetry networks achieve gains exceeding 20 percent in zero-shot transfer to unseen robot morphologies, suggesting that the learned representations capture transferable physical structure rather than dataset-specific patterns.