Strengthening Social Security Act of 2019 This bill expands benefits, and increases specified taxes, related to the Old-Age, Survivors, and Disability Insurance 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 $132,900.