We investigate a simple generalization of the metric exponential $f(R)$ gravity theory that is cosmologically viable and compatible with solar system tests of gravity. We show that, as compared to other viable $f(R)$ theories, its steep dependence on the Ricci scalar $R$ facilitates agreement with structure constraints, opening the possibility of $f(R)$ models with equation-of-state parameter that could be differentiated from a cosmological constant ($w_{de}=-1$) with future surveys at both background and perturbative levels.

Comment: v3: matches the version accepted by PRD