Promotion and Expansion of Private Employee Ownership Act of 2013 - Amends the Internal Revenue Code to extend to all domestic corporations, including S corporations, provisions allowing deferral of tax on gain from the sale of employer securities to an S corporation-sponsored employee stock ownership plan (ESOP).

Directs the Secretary of the Treasury to establish the S Corporation Employee Ownership Assistance Office to foster increased employee ownership of S corporations.

Amends the Small Business Act to define "ESOP business concern" and allow such a concern to continue to qualify for loans, preferences, and other programs under such Act.