Someone who wants to sell you a Superball claims that it will bounce to a height greater than the height from which it is dropped. Can this be?

No

Explanation:

Unless there are other external forces, this will never be true. Because according to energy conservation, potential energy will be converted to kinetic energy as the ball falls down (so it loses height and gain speed). And vice versa, kinetic to potential when it bounces back. So the potential energy after must be the same (or smaller if losing heat to external environment), so it can only get the the same height or less, but not more.