A Study of Sacituzumab Govitecan in Combination With Cetuximab in People With Head and Neck Squamous Cell Cancer (HNSCC)

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of squamous cell carcinoma of the head and neck arising from the sinuses, nasal cavity, oral cavity, oropharynx, hypopharynx, and larynx. Other sites not listed will be subject to PI discretion. * Advanced disease (Stage IV or M1 disease) not amenable to curative local therapy with surgery and/or radiation based approaches * Progression on first line anti-PD(L)1 therapy with or without chemotherapy or as part of a combination in a clinical trial * HPV status for oropharynx primary must be previously confirmed or can be performed on available archival or fresh biopsy via p16 immunohistochemistry or HPV specific testing via PCR or RNA ISH. Patients are able to enroll and initiate treatment so long as this is in progress. Exceptions may be made after discussion and review with P.I. * Have measurable disease per RECIST v1.1 criteria. Tumor lesions situated in previously radiated area may be utilized if they are measurable and progression has been demonstrated in these lesions. * Male or female patients 18 years of age or older on the day of consent. * ECOG Performance Status of 0 to 1. * Adequate hematologic function within 30 days prior to registration, defined as follows: * Absolute neutrophil count (ANC) ≥ 1,500 cells/mm3 * Platelets ≥ 100,000 cells/mm3 * Hemoglobin ≥ 9.0 g/dl; Note: The use of transfusion or other intervention to achieve Hgb ≥ 9.0 g/dl is acceptable * Adequate renal function within 30 days prior to registration, defined as follows: o Serum creatinine \< 2.0 x upper limit of normal (ULN) or creatinine clearance (CCr) ≥ 30 ml/min determined by 24-hour collection or estimated by Cockcroft-Gault formula: CCr male = \[(140 - age) x (wt in kg)\] \[(Serum Cr mg/dl) x (72)\] CCr female = 0.85 x (CrCl male) * Adequate hepatic function within 30 days prior to registration, defined as follows: * Total bilirubin ≤ 1.5 × ULN (except for unconjugated hyperbilirubinemia or Gilbert's syndrome). Direct bilirubin ≤ ULN for participants with total bilirubin levels \> 1.5 × ULN. * AST and ALT \< 2.5 x the upper limit of normal * Albumin ≥ 3 g/dL * International Normalized Ratio (INR) or Prothrombin Time (PT) ≤ 1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants. * Activated Partial Thromboplastin Time (aPTT) or Partial Thromboplastin Time (PTT) ≤ 1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants. * Female patients are eligible to participate if they are not pregnant, not breastfeeding and at least one of the following conditions applies: * Not a woman of childbearing potential * A woman of childbearing potential who agrees to use highly effective contraception from signing of the ICF through six months after the last study treatment administration. Notes: i. Female of childbearing potential are those who have not been surgically sterilized or have not been free from menses for \>1 year. ii. Highly effective contraception methods include: * Total abstinence * Male or female sterilization * Combination of any 2 of the following categories (Categories 1+2, 1+3, or 2+3): * Category 1: Use of oral, injected, or implanted hormonal methods of contraception. * Category 2: Placement of an intrauterine device or intrauterine system. * Category 3: Category 3: Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository. * A female participant who is of childbearing potential must have a negative serum β-human chorionic gonadotrophin (β-hCG) pregnancy test within 72 hours prior to the first administration of study treatment or be surgically/biologically sterile (hysterectomy or bilateral oophorectomy) or postmenopausal. Note: Postmenopausal females are defined as those who are: * Age \> 50 years with amenorrhea for ≥ 12 months. * Age ≤ 50 years with six months of spontaneous amenorrhea and follicle stimulating hormone level within postmenopausal range (\> 40 mIU/mL). * Male patients must agree to use contraception and refrain from sperm and egg donation from the time period between signing of the ICF and through five months after the last dose of study drug * The subject must provide voluntary study-specific informed consent prior to study entry. Exclusion Criteria: * Patients must not have received more than 2 prior line of systemic treatment (i.e. in the second or third line of treatment) in the recurrent/metastatic setting. o Ambiguity regarding lines of treatment a patient has received will be subject to PI review and approval. * Patients with previous severe infusion or allergic reactions to EGFR antibody based therapy that is deemed unsafe for re-challenge based on assessment by PI and/or consultation with allergy/immunology. * Patients who have previously received topoisomerase I inhibitors for HNSCC * Patients who have a confirmed or suspected diagnosis (subject to P.I. discretion) of Gilbert's Syndrome * Have had a prior anti-cancer biologic agent, chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1. * Have not recovered (ie, ≤ Grade 1) from AEs due to a previously administered agent. * Note: Subjects with ≤ Grade 2 neuropathy or ≤ Grade 2 alopecia are exceptions to this criterion and may qualify for the study. * Note: If subjects underwent major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study drug. * Note: Subjects with Grade ≤ 2 immune-mediated toxicities (except colitis which must be recovered, \< Grade 1) related to immunotherapy and/or radiation treatment that are long lasting, but stable on treatment and not requiring agents that are excluded by this protocol may qualify for the study. * Patients with simultaneous primary cancers aside from HNSCC will be excluded unless otherwise approved by PI. * Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free for 3 years or if cure rate for the malignancy treated at 5 years is estimated to be 90% or greater, unless otherwise approved by PI * Severe, active co-morbidity defined as the following: * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Transmural myocardial infarction within the last 6 months * Acute infection requiring intravenous therapy at the time of registration * Chronic Obstructive Pulmonary Disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy within 30 days of registration * Hepatic Insufficiency resulting in clinical jaundice and/or coagulation defect * Have known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they have stable CNS disease for at least 4 weeks prior to the first dose of study drug and all neurologic symptoms have returned to baseline, no evidence of new or enlarging brain metastases and are taking ≤ 20 mg/day of prednisone or its equivalent. All subjects with carcinomatous meningitis are excluded regardless of clinical stability. * Have active chronic inflammatory bowel disease (ulcerative colitis, Crohn's disease), immune-mediated colitis, or gastrointestinal (GI) perforation within 6 months of C1D1. * Known acquired immunodeficiency syndrome due to untreated/poorly controlled human immunodeficiency virus. Other diagnosed immunodeficiency syndromes or disorders will require the review and approval of the site PI. * Positive test for hepatitis B surface antigen (HBsAG) or hepatitis C virus antibody (anti-HCV), indicating acute or chronic infection. Patients who test positive for anti-HCV but negative for HCV ribonucleic acid (RNA) are permitted to enroll. * Herbal remedies known to potentially interfere with major organ function within 28 days prior to the first dose of study treatment, unless agreed otherwise between the PI and treating investigator. * Female patients who are pregnant, breastfeeding, or plan on becoming pregnant during the study.