Key Inclusion Criteria:  Histologically or cytologically confirmed metastatic or locally recurrent HNSCC that is considered incurable by local therapies  Safety Run-in Cohort 1 and Phase 2 Cohorts 1  HNSCC per protocol specified inclusion criteria regardless of PD-L1 status HNSCC per protocol specified inclusion criterion with a PD-L1 CPS ≥ 1  Safety Run-in Cohort 2 and Phase 2 Cohort 3  Histologically or cytologically confirmed locally advanced/mHNSCC regardless of PD-L1 status with at least 1 and no more than 2 lines of prior systemic anticancer therapy in the locally advanced/metastatic setting  Key Exclusion Criteria:  Active central nervous system (CNS) disease (individuals with asymptomatic and stable, treated CNS lesions who have been off corticosteroids, radiation, or other CNS-directed therapy for at least 4 weeks are not considered active) History of (noninfectious) pneumonitis that required steroids or current pneumonitis  Safety Run-in Cohort 1, Pre-expansion Safety Run-in Cohort for Magrolimab + Pembrolizumab (if Applicable), and Phase 2 Cohorts 1 and 2  Prior treatment with any of the following:  Anti-programmed cell death protein 1 or anti-PD-L1 checkpoint inhibitors Anti-cytotoxic T-lymphocyte-associated protein 4 checkpoint inhibitors 5-FU and platinum-based chemotherapy (Safety Run-in Cohort 1 and Phase 2 Cohorts 1 only)  Safety Run-in Cohort 2 and Phase 2 Cohort 3  Progressive disease within 6 months of completion of curatively intended systemic treatment for locally advanced/mHNSCC Prior treatment with a taxane  Note: Other protocol defined Inclusion/Exclusion criteria may apply.