Paycheck Protection Program Small Business Enhancement Act This bill extends the duration of, authorizes subsequent loans under, and otherwise modifies the Paycheck Protection Program established to support small businesses in response to COVID-19 (i.e., coronavirus disease 2019). Specifically, the bill extends the Paycheck Protection Program through December 31, 2020. It also authorizes a recipient of a paycheck protection loan to apply for a subsequent loan made under the same terms, conditions, and process, and for which the recipient shall be eligible for forgiveness in the same manner, as an initial paycheck protection loan. Further, the bill expands program eligibility to include (1) organizations such as business leagues and chambers of commerce, and (2) franchisors or franchisees that employ not more than 500 employees per physical location. The bill also prohibits the use of program amounts for lobbying activities and makes eligible expenses tax deductible. In addition, the bill provides for an abbreviated process for forgiveness of a paycheck protection loan that is not more than $150,000.