Spaceplates are nonlocal optical devices with the potential to reduce the form factor of optical systems, but current implementations are limited in performance and ability to correct for optical aberrations. We introduce a new class of multifunctional spaceplates, designed using gradient-based freeform optimization, which exhibit exceptional efficiencies, compression ratios, and aberration correcting capabilities. We show that such spaceplates can serve as correctors for metasurfaces and refractive optical elements, and we demonstrate that multifunctional spaceplates can extend to support multispectral, Petzval field curvature, and spherical aberration correction. We anticipate that these spaceplate concepts will enable the realization of ultracompact optical systems.