A Study of Amivantamab Alone or in Addition to Other Treatment Agents in Participants With Head and Neck Cancer

Inclusion Criteria: * Cohorts 1 to 5: Have histologically or cytologically confirmed recurrent/metastatic head and neck squamous cell carcinoma (R/M HNSCC) that is considered incurable by local therapies or for Cohort 6: have histologically or cytologically confirmed locally advanced (L/A) HNSCC that is considered curable by surgery Acceptable prior lines of therapy will be determined according to specific cohort 1, 2, 3A and 3B: (a) The eligible primary tumor locations are the oropharynx, oral cavity, hypopharynx, or larynx; (b) Any known p16 status of tumor must be negative (Note: All participants with an oropharyngeal tumor must have results of p16 status, per local testing); (c) Participants must provide local testing results of programmed cell death ligand 1 (PD-L1) status, if available; Cohort 4: (d) Patients must have primary tumor location in oropharynx. Unknown primary tumors are not included (e) Primary tumor must be HPV-positive, confirmed by positive p16 test or high-risk human papillomavirus (HPV) in-situ hybridization (ISH) in tissue (current or archival) (f) Participants must provide local testing results of PD-L1 status, if available; Cohort 5 (g) The eligible primary tumor locations are the oropharynx, oral cavity, hypopharynx, or larynx; (h) HPV status must be known (either positive or negative) for patients with primary tumor location in oropharynx with p16 test or high-risk HPV ISH in tissue; (i) Participants must provide local testing results of PD-L1 status; Cohort 6: (j) The eligible primary tumor locations are the oropharynx, oral cavity, hypopharynx, or larynx; (k) Any known p16 status of tumor must be negative Note: All participants with an oropharyngeal tumor must have results of p16 status, per local testing Participants must provide local testing results of PD-L1 status (l) Participants must have Stage III or IVa disease (American Joint Committee on Cancer Staging Manual, 8th edition). Participants must have resectable disease * Participants in Cohorts 1, 2, 3B, 4 and 5 must have measurable disease according to RECIST version 1.1. Participants in Cohort 3A and Cohort 6 must have evaluable disease (defined as having at least 1 non-target lesion according to RECIST version 1.1. * Cohorts 1, 2, 3A, 3B, 4, and 5 only: Toxicities from previous anticancer therapies should have resolved to baseline levels or to Grade 1 or less prior to the first dose of study treatment (except for alopecia or post-radiation skin changes \[any grade\], Grade less than or equal to \[\<=\]2 peripheral neuropathy and Grade \<=2 hypothyroidism stable on hormone replacement) * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 * Participant must have adequate organ and bone marrow function as follows, without history of red blood cell transfusion, platelet transfusion, or use of granulocyte colony-stimulating factor within 7 days prior to the date of the laboratory test. Participants should have: a) Hemoglobin \>=9 grams per deciliter (g/dL); b) Neutrophils \>=1.5 x 10\^3/mcg; c) Platelets \>=100 x 10\^3/mcg Exclusion Criteria: * Uncontrolled illness including any medical history or current (non-infectious) interstitial lung disease (ILD)/ pneumonitis/ pulmonary fibrosis, or where suspected ILD/pneumonitis/pulmonary fibrosis cannot be ruled out by imaging at screening * Participant with untreated brain metastases leptomeningeal disease, or spinal cord compression not definitively treated with surgery or radiation * Participant with a history of clinically significant cardiovascular disease * Received prior chemotherapy, targeted cancer therapy, immunotherapy, or treatment with an investigational anticancer agent within 2 weeks or 4 half-lives, whichever is longer, before the first administration of study treatment. The maximum required washout is 28 days * Received radiotherapy for palliative purposes within 7 days of the first administration of study treatment