The New York Stock Exchange is seeking regulators' approval for a new disaster-recovery plan that would allow the exchange to close while trading in Big Board-listed stocks shifts to an all-electronic platform.

The NYSE proposal, filed with the Securities and Exchange Commission late Monday, would elevate the backup role of NYSE Euronext's all-electronic Arca exchange. Eventually, the exchange group aims to enable the NYSE itself to trade entirely via computer systems, allowing the exchange to do business without its storied trading floor if need be.