Increase Overall Resolution With Multiple Images?

Been wondering about this for a while. Is there a program out there that will allow you to stack multiple images to increase the resolution and detail? I'm not talking about averaging the detail from a stack of images, but interpolating them into a new, larger image with near the level of sharpness of the original, with a little more detail. For example, taking 10x 16MP images, and processing them to come to 1x 24-32MP image. Any ideas?