Symmetry plays a central role in modern physics, from classifying quantum states to characterizing phases of matter through spontaneous symmetry breaking. In interacting fermionic systems with multiple internal degrees of freedom, however, determining the full continuous symmetry group and classifying possible order parameters remain challenging. In this work, we present a systematic framework for analyzing continuous symmetries and identifying candidate order parameters in such systems, without assuming the irreducible matter-field content or the preserved symmetry group in advance. By mapping the Hamiltonian to a Majorana representation, we obtain the generators of continuous symmetries from the Lie algebra of operators that commute with the Hamiltonian. We then identify the structure of this Lie algebra using the theory of semisimple Lie algebras. Building on representation theory, we further develop a systematic method for exhaustively enumerating candidate order parameters. By decomposing the exterior-power representations induced by the symmetry algebra on the Majorana space and incorporating discrete lattice symmetries, we classify these order parameters according to the symmetries they break. To demonstrate the power of the framework, we first apply it to the single-layer Hubbard model on a honeycomb lattice as a benchmark and recover the well-known $\mathrm{SO}\left(4\right)$ symmetry with $\mathfrak{su}\left(2\right)\oplus \mathfrak{su}\left(2\right)$ symmetry algebra. We then apply it to a bilayer spin-$1/2$ fermion model on a honeycomb lattice with Heisenberg exchange and density-density interlayer couplings, uncovering a $\mathrm{Spin}\left(5\right)\times \mathrm{U}\left(1\right)/{\mathbb{Z}}_2$ symmetry with $\mathfrak{so}\left(5\right)\oplus \mathfrak{u}\left(1\right)$ symmetry algebra. Within this setting, we systematically classify all candidate bilinear order parameters and reveal a rich landscape of potentially competing phases. The same framework has also been applied to a closely related bilayer model with pure Heisenberg interlayer coupling, which possesses an $\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)/{\mathbb{Z}}_2$ symmetry with $\mathfrak{su}\left(2\right)\oplus \mathfrak{su}\left(2\right)\oplus \mathfrak{su}\left(2\right)$ symmetry algebra [He et al., arXiv:2603.18278].

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• Order parameters
• Quantum phase transitions
• Continuous symmetries