This disclosure provides a method of treating an HPV16-associated cancer in an individual, the method comprising administering to the individual a T-cell modulatory protein (TMP) and an PD-(L)1 CPI that targets PD-1 or PD-L1, i.e., a “PD-(L)1 CPI”, where (A) the individual previously was determined to have progressive disease based on RECIST 1.1 criteria following (i) monotherapy with a PD-(L)1 CPI, or (ii) combination therapy comprising treatment with a PD-(L)1 CPI and a therapeutic agent other than the TMP, or (B) where the individual has a PD-L1 Combined Positive Score (PD-L1 CPS) of 0 or more than 0 but less than 1.