We highly recommend our customers to skip the staining and opt for a top clear coat instead. A clear finished veneer provides a nice natural colour without obscuring any grains.
Nevertheless, since veneer is real wood, it can accept stains and finishes much like solid wood. The choices of stains and finishes are many and each combination can yield a different outcome. Ultimately, it is the onus of the customer/person fabricating the job to decide which stain (if any) is best for the project.