Promotion and Expansion of Private Employee Ownership Act of 2021 This bill expands tax incentives and federal assistance for employee stock ownership plans (ESOPs) that are sponsored by S corporations. The bill extends to all domestic corporations, including S corporations, provisions allowing deferral of tax on gain from the sale of employer securities to an ESOP. The Department of the Treasury must establish the S Corporation Employee Ownership Assistance Office to foster increased employee ownership of S corporations. The bill defines an ESOP business concern and allows such a concern to continue to qualify as a small business for the purposes of programs under the Small Business Act. An ESOP business concern is a business concern that was a small business concern eligible for a loan, preference, or other program under the Small Business Act before more than 49% of the business concern was acquired by an ESOP.