We show from simulations that a limited mobility solid-on-solid model of kinetically rough surface growth exhibits extended self-similarity analogous to that found in fluid turbulence. The range over which scale-independent power-law behavior is observed is significantly enhanced if two correlation functions of different order, such as those representing two different moments of the difference in height between two points, are plotted against each other. This behavior, found in both one and two dimensions, suggests that the relative″ exponents may be more fundamental than the absolute″ ones.