Pell Plus Act of 2023 This bill establishes the Pell Plus program to award an additional Federal Pell Grant (i.e., a Federal Pell Plus Grant), which shall be matched by the participating institution of enrollment, to eligible students. A student is eligible to receive a Federal Pell Plus Grant if the student (1) is enrolled in their first undergraduate course of study at a Pell Plus institution, (2) is maintaining progress toward completion of their course of study in no more than four academic years, and (3) has completed at least four semesters (or the equivalent) of such course of study. Further, the bill outlines the requirements for an institution to participate as a Pell Plus institution, including that the institution must notify students whether they are maintaining progress toward completion of their course of study. The bill directs the Department of Education (ED) to award a Federal Pell Plus Grant to an eligible student in an amount equal to the student's Federal Pell Grant award. If the student's combined Federal Pell Grant and Federal Pell Plus Grant exceed the cost of attendance, then ED must reduce the amount of the student's Federal Pell Plus Grant. The bill specifies that these Federal Pell Plus Grants must count toward current duration limits.