A company can list its shares on more than one exchange, which is often referred to as a dual-listing. A stock can trade on any exchange in which it is listed. However, companies must meet all of the exchange's listing requirements and pay for any associated fees in order to be listed.
Short-answer: Yes, NASDAQ has a dual listing program that allows stocks traded in the NYSE to list on the NASDAQ stock market as well. However, it must need to meet all of the exchange's listing requirements and settle associated fees.