Paycheck Protection Program Extension and Modification Act of 2020 This bill extends through December 31, 2020, the Paycheck Protection Program established to support small businesses in response to COVID-19 (i.e., coronavirus disease 2019), and it authorizes additional lending under the program. Specifically, the bill authorizes an additional program loan to be made to a prior recipient of a paycheck protection loan. Such additional loan shall be (1) used for allowable expenses under the program, (2) guaranteed in the same manner as a paycheck protection loan, and (3) eligible for forgiveness under the program.