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
* Should not have had prior systemic therapy administered in the recurrent or metastatic setting.
* Eligible primary tumor locations include oropharynx, oral cavity, hypopharynx, and larynx. Nasopharynx is not included.
* HNSCC per protocol specified inclusion criteria regardless of PD-L1 status
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
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.