The desire for cameras with smaller form factors has recently lead to a push for exploring computational imaging systems with reduced optical complexity such as a smaller number of lens elements. Unfortunately such simplified optical systems usually suffer from severe aberrations, especially in off-axis regions, which can be difficult to correct purely in software. In this paper we introduce Fovea Stacking , a new type of imaging system that utilizes emerging dynamic optical components called deformable phase plates (DPPs) for localized aberration correction anywhere on the image sensor. By optimizing DPP deformations through a differentiable optical model, off-axis aberrations are corrected locally, producing a foveated image with enhanced sharpness at the fixation point - analogous to the eye's fovea. Stacking multiple such foveated images, each with a different fixation point, yields a composite image free from aberrations. To efficiently cover the entire field of view, we propose joint optimization of DPP deformations under imaging budget constraints. Due to the DPP device's non-linear behavior, we introduce a neural network-based control model for improved alignment between simulation-hardware performance. We further demonstrated that for extended depth-of-field imaging, fovea stacking outperforms traditional focus stacking in image quality. By integrating object detection or eye-tracking, the system can dynamically adjust the lens to track the object of interest-enabling real-time foveated video suitable for downstream applications such as surveillance or foveated virtual reality displays