Human papillomavirus positive (HPV+) tonsillar and base of tongue squamous cell carcinoma (TSCC/BOTSCC) have a favorable outcome, but upon relapse, survival is poor and new therapeutical options are needed. Recently, we found synergistic effects by combining the food and drug administration approved (FDA) phosphoinositide 3-kinase (PI3K) and fibroblast-growth-factor-receptor (FGFR) inhibitors BYL719 and JNJ-42756493 on TSCC cell lines. Here this approach was extended and Cyclin-Dependent-Kinase-4/6 (CDK4/6) and Poly-ADP-ribose-polymerase (PARP) and WEE1 inhibitors PD-0332991, and MK-1775 respectively were also examined. HPV+ CU-OP-2, -3, -20, and HPV- CU-OP-17 TSCC cell lines were treated with either BYL719 and JNJ-42756493, PD-0332991 BMN-673 and MK-1775 alone or in different combinations. Viability, proliferation, and cytotoxicity were followed by WST-1 assays and the IncuCyte S3 Live® Cell Analysis System. All inhibitors presented dose-dependent inhibitory effects on tested TSCC lines. Synergy was frequently obtained when combining CDK4/6 with PI3K inhibitors, but only sometimes or rarely when combining CDK4/6 with FGFR inhibitors or PARP with WEE1 inhibitors. To conclude, using CDK4/6 with PI3K or FGFR inhibitors, especially PD-0332991 with BYL719 presented synergy and enhanced the decrease of viability considerably, while although dose dependent responses were obtained with PARP and WEE1 inhibitors (BMN-673 and MK-1775 resp.), synergy was rarely disclosed.