Our work resonates in the context of nonlinear elliptic problems, including supersolutions to fully nonlinear elliptic equations and viscosity classes. The main goal of our research is to generalize recent results for equations in which the ingredients are merely unbounded. In particular, we prove an abstract result, referred to in the literature as flipping geometry, ensuring that one-sided geometric control yields two-sided estimates for functions satisfying general conditions. With this result, we prove a series of regularity theorems under natural assumptions. Among the main ingredients used in our findings, one meets a weak Harnack-type inequality and maximum principles.