Study of Safety and Tolerability of BCA101 Monotherapy and in Combination Therapy in Patients With EGFR-driven Advanced Solid Tumors

Inclusion Criteria: * Patient must have measurable disease amendable to biopsy and be willing to undergo both a pre-treatment and on-treatment biopsy, as well as provide archival tumor if available from the primary tumor (a paraffin embedded tumor tissue block sufficient to obtain at least 10 sections of 4 to 5 micrometer thickness). * Patient must have a performance status of ≤1 on the Eastern Cooperative Oncology Group Performance Scale. * Patients must have evaluable or measurable disease (computed tomography \[CT\]/magnetic resonance imaging \[MRI\] scans performed within 21 days before the screening visit are acceptable) demonstrating measurable disease, i.e., at least 1 unidimensional measurable lesion as defined by Response Evaluation Criteria in Solid Tumors, Version 1.1 (RECIST 1.1) and Immune Response Evaluation Criteria in Solid Tumors (iRECIST). * Tumor eligibility: PART B (Cohort expansion): 1. Single agent BCA101 - patients with the following tumor type will be eligible: • Expansion Cohort 1: Cutaneous Squamous Cell Carcinoma (CSCC) - i. patients must have received (or been intolerant to or ineligible for) prior anti-PD-1 therapy in the metastatic or locally advanced setting. ii. No prior history of treatment with anti-EGFR antibodies in the unresectable/metastatic setting (prior treatment with radiotherapy in the adjuvant setting is allowed). 2. Combination BCA101 and pembrolizumab - patients with the following tumor types will be eligible: • Expansion Cohort 2: Head and Neck Squamous Cell Carcinoma (HNSCC), metastatic or unresectable, recurrent with a Combined Positive Score (CPS) equal to or greater than 1, as determined by an CLIA-approved laboratory test. Primary tumor locations of oropharynx, oral cavity, hypopharynx, or larynx. Participants may not have a primary tumor site of nasopharynx (any histology). i. Patients must have no prior systemic therapy administered in the recurrent or metastatic setting (with the exception of systemic therapy completed \>6 months prior if given as part of multimodal treatment for locally advanced disease) or prior history of immune checkpoint inhibitors with the exception of neoadjuvant therapy (\>6 months prior to study drug initiation). No prior history of anti-EGFR antibodies (with the exception of radiosensitizing agents and multimodal treatment for locally advanced disease). ii. Patients must provide tissue for PD-L1 biomarker analysis from a core or excisional biopsy (fine needle aspirate is not sufficient): A newly obtained biopsy (within 90 days prior to start of study treatment) is preferred but an archival sample is acceptable. iii. Patients must have results from testing of human papillomavirus (HPV) status for oropharyngeal cancer * Expansion Cohort 3: Squamous Carcinoma of the Anal Canal (SCAC), locally advanced/unresectable or metastatic. i. Patients must have received (or been intolerant to or ineligible for) at least 1 prior line of chemotherapy and received no more than 2 prior lines of systemic treatments for treatment of unresectable and/or metastatic disease. No prior history of immune checkpoint inhibitors. * Expansion Cohort 5: Squamous Non-Small Cell Lung Cancer (SqNSCLC) i. Patients must have a histologically or cytologically confirmed diagnosis of stage IV (AJCC 8th edition) squamous NSCLC. Patients with mixed histology (e.g., adenosquamous) are not allowed. ii. Patients must have progressed on one prior systemic therapy in the metastatic setting. iii. No prior history of treatment with anti-EGFR antibodies in the metastatic setting. • Expansion Cohort 6: Head and Neck Squamous Cell Carcinoma (HNSCC), metastatic or unresectable, recurrent with a Combined Positive Score (CPS) less than 1, as determined by PD-L1 IHC 22C3 pharmDx. 3. Randomized to either ficerafusp alfa alone or in combination with pembrolizumab • Expansion Cohort 9: Colorectal cancer (CRC) i. Patients must have received at least 2 and no more than 3 prior lines of systemic therapy including two standard treatment regimens. Exclusion Criteria: * For Part A: Exposure to anti-EGFR antibodies within 4 weeks of the first dose of study drug. * Prior treatment with any anti-TGFβ therapy. * Prior history of Grade ≥ 2 intolerance or hypersensitivity reaction to cetuximab or other anti-EGFR therapy or other murine proteins or prior discontinuation of therapy in the setting of toxicity related to treatment. * Pregnant or breastfeeding women. * Any condition requiring systemic treatment with either corticosteroids (\>10 mg daily of prednisone or equivalent) or other immunosuppressive medication within 14 days prior to the first dose of study drug, with the exception of topical, intranasal, intrabronchial, or ocular steroids. * Known history of a hematologic malignancy (or solid tumor other than the ones indicated for this study), unless the patient has undergone potentially curative therapy with no evidence of that disease for 2 years. Does not include tumors with a negligible risk of metastasis or death (e.g. adequately treated basal or squamous cell carcinoma, stage 1 prostate cancer, or carcinoma in situ of the cervix or carcinoma in situ of the breast). Subjects enrolling in the CSCC cohort may have chronic lymphocytic leukemia as long as the patient is not on active treatment. * Known cases of human immunodeficiency virus (HIV) are excluded if patients have a CD4+ T-cell (CD4+) count \<250 cells/uL. To ensure that effective antiretroviral therapy (ART) is tolerated and that toxicities are not confused with investigational drug toxicities, trial participants should be on established ART for at least four weeks and have an HIV viral load less than 400 copies/mL prior to enrollment. * Patients with chronic HBV infection with active disease who meet the criteria for anti-HBV therapy and are not on a suppressive antiviral therapy prior to initiation of study treatment * Patients with a known history of hepatitis C who have not completed curative antiviral treatment or have a HCV viral load above the limit of quantification