Can a cushion vinyl floor be laid over another cushion vinyl floor?

It is possible, but it's not the best practice. If you can easily remove the existing vinyl, then do so. If the vinyl won't peel up, then you should consider two possibilities: Remove the vinyl along with the wood underlayment (or scrape it off if your subfloor is concrete), or install new wood underlayment on top of the existing vinyl.

A third possibility is this: If the existing vinyl is securely glued to the floor, you could apply an embossing leveler (cement-based product) in a very thin skim coat over the vinyl. This seals in any stains, levels the floor, and gives the new vinyl a nice, smooth surface to lay over (or a good surface for vinyl glue to adhere to).

Most flooring manufacturers will not honor the warranty on their vinyl if it is installed over existing vinyl, unless you do the embossing leveler step above.