Inclusion Criteria:

• Provide written informed consent.

Cancers as follows - Cohort 1:

• Histologically or cytologically confirmed recurrent locally and/or metastatic head and neck squamous cell carcinoma with Combined Positive Score (CPS) ≥ 1 as determined by an FDA approved test.
  • Note: A multi-disciplinary group (including a surgeon and radiation oncologist) must agree that the patient is not a candidate for locoregional therapy.

Cohort 2:

• Histologically or cytologically confirmed locally advanced or metastatic cutaneous squamous cell carcinoma not amenable to definitive surgery or radiation.

Cohort 3:

• Histologically or cytologically confirmed locally advanced or metastatic cutaneous squamous cell carcinoma not amendable to definitive surgery or radiation. Patients' disease has progressed despite at least 2 months of anti-PD1 therapy.
• At least one site of disease accessible to light illumination.
• Measurable disease by modified RECIST 1.1.
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
• No prior systemic therapy administered in the recurrent and/or metastatic setting (with the exception of systemic therapy completed ≥ 6 months prior if given as part of multimodal treatment for locally advanced disease).
• Adequate organ function.
• Female patients of childbearing potential must have a negative pregnancy test at screening and must be willing to use 2 methods of highly effective birth control while on study or be surgically sterile, or abstain from heterosexual sexual activity for the course of the study through 120 days after the last dose of anti-PD1 treatment.
• Male participants must agree to use a highly effective method of contraception starting with the first dose of study medication through 120 days after the last dose of anti-PD1 treatment.

Exclusion Criteria:

• Prior therapy with an anti-PD1 or anti-PD-L1 (Cohort 1 and 2 only).
• Radiation therapy (or other non-systemic therapy) within 4 weeks prior to study Day 1 or not fully recovered from adverse events due to a previously administered treatment.
• Receiving chronic systemic steroid therapy (in doses exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 14 days prior to Cycle 1 Day 1.
• Diagnosed and/or treated for additional malignancy within 2 years prior to study Day 1, except for, curatively treated basal cell carcinoma of the skin, squamous cell carcinoma of the skin and/or curatively resected in situ cervical and/or breast cancers.
• History of significant (≥ Grade 3) cetuximab infusion reactions.
• Prior allogeneic tissue/solid organ transplant.
• Known or active central nervous system metastases and/or carcinomatous meningitis.
• Active autoimmune disease that has required systemic treatment in past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs).
• Evidence of interstitial lung disease or current active, noninfectious pneumonitis.
• Active infection requiring systemic therapy.
• Known or active bacterial, viral, and fungal infection including tuberculosis, active Hepatitis B (e.g., HBsAg reactive), or Hepatitis C (e.g., RNA [qualitative] is detected).
• Known history of testing positive for human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS)-related illness.
• Received a live vaccine within 30 days of study Day 1.
  • Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.
• Patients expecting to breastfeed during the study and through 120 days after the last dose of study treatment.
• Major surgery or significant traumatic injury ≤ 28 days before study day 1, or anticipation of the need for major surgery during the course of study treatment.
• Currently participating or participated in a study of an investigational agent and received study therapy (including RM-1929 or ASP-1929 PIT studies), or used an investigational device within 4 weeks of study Day 1.
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.