  The Rabi model describes the simplest nontrivial interaction between a
few-level system and a bosonic mode, featuring in multiple seemingly unrelated
systems of importance to quantum science and technology. While exact
expressions for the energies of this model and its few-mode extensions have
been obtained, they involve roots of transcendental functions and are thus
cumbersome and unintuitive. Utilizing the symmetric generalized rotating wave
approximation (S-GRWA), we develop a family of approximations to the energies
of the two-mode two-photon Rabi model. The simplest elements of the family are
analytically tractable, providing good approximations in regimes of interest
such as ultra- and deep-strong coupling. Higher-order approximate energies can
be used if more accuracy is required.
