Strengthening Social Security Act of 2021 This bill expands benefits, and increases specified taxes, related to the Social Security retirement and disability benefits program. Changes to benefits include (1) increasing the primary insurance amount for certain beneficiaries, (2) calculating cost-of-living adjustments by using a price index that tracks the spending patterns of older consumers, and (3) establishing an alternative benefit for widows or widowers in two-income households. Changes to taxes include phasing out the cap on earnings subject to the Social Security payroll tax. Under current law, the maximum amount subject to this tax is $142,800.