  We revisit the classical aspects of $\mathcal{N}=(2,2)$ supersymmetric sigma
models with Hermitian symmetric target spaces, using the so-called Gross-Neveu
(first-order GLSM) formalism. We reformulate these models for complex
Grassmannians in terms of simple supersymmetric Lagrangians with polynomial
interactions. For maximal isotropic Grassmannians we propose two types of
equivalent Lagrangians, which make either supersymmetry or the geometry of
target space manifest. These reformulations can be seen as current-current
deformations of curved $\beta \gamma$ systems. The $\mathsf{CP}^{1}$
supersymmetric sigma model is our prototypical example.
