Summary: This article explores the possibility of another kind of superresolution functionality that exists in superoscillatory functions besides the “faster than Fourier” feature. We posit the ability to resolve images with resolution beyond the wavelength of light used via the exponentially rising and falling parts of superoscillatory and related functions. We give some preliminary results that this technique can indeed be useful using intensity contrast imaging. The exponential growth or decay of these functions can give higher resolution of the image, provided the rate of falloff is faster than the smallest wavenumber of the light that is used: “supergrowth”. One limitation of this proposal is the high dynamic range the detector would need to possess to map out several decades of intensity. An outstanding question is to find the optimal image reconstruction method using a superoscillatory point spread function that makes optimal use of the function’s unique properties. We give a number of conjectures about this new kind of supergrowth imaging technique as an outlook for future research.