  The hidden $\mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model
(AQRM) has recently been revealed via a systematic construction of the
underlying symmetry operator. Based on the AQRM result, we propose an ansatz
for the general form of the symmetry operators for AQRM-related models.
Applying this ansatz we obtain the symmetry operator for three models: the
anisotropic AQRM, the asymmetric Rabi-Stark model (ARSM) and the anisotropic
ARSM.
