• 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):

⁃ 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).

⁃ 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.

⁃ 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.