Are there maximum/minimum values for a* and b* like the min and max for L*?
No, there are not specific limits. The limits for given types of materials (or lights) would depend on both their material properties and the viewing conditions. You might look at the MacAdam Limits to see what some theoretical limits for reflecting objects look like. The a*b* limits depend on the hue and lightness of the object. In imaging applications, limits for 8-bit encoding are often set as the range from -127 to +128 in both a* and b*. This is adequate to cover the gamut of most systems.
