Is there a way for a laser to work across a range of colors?
Through the magic of nonlinear optics you can buy a super supercontinuum laser which outputs light in a very broad spectrum, typically 400 nm to 1,700 nm.

https://en.wikipedia.org/wiki/Supercontinuum



A small wavelength band may be selected with an acousto-optic modulator

See one in action tuning over the wavelength band:
https://www.youtube.com/watch?v=I7_E_sOOl9U