Inclusion Criteria:  Patients must be diagnosed with resectable primary or recurrent locoregional head and neck squamous cell carcinoma (HNSCC) or cutaneous squamous cell carcinoma (cuSCC) that is eligible for standard of care surgical resection. At least one target tumor must be amenable to photoimmunotherapy with the PIT690 Laser System and imaging with the Fluorescence Imaging System. Measurable disease by RECIST 1.1, as assessed by the Investigator Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 at the time of screening. Adequate organ function laboratory values as described in the protocol (all screening labs should be performed ≤ 14 days of Day 1) Female patients of childbearing potential must not be pregnant (confirmed by negative pregnancy test [urine or serum] at screening) or breastfeeding and must be willing to use a method of highly effective birth control, or practice abstinence throughout the study and for 60 days after the last dose of ASP-1929. Females of childbearing potential are those who have not been surgically sterilized or have not been free from menses for > 1 year. Male patients must be sterile or agree to use an adequate method of contraception or practice abstinence throughout the study and for 60 days after the last dose of ASP-1929.  Exclusion Criteria:  Receiving any other investigational agents or who have received local (including radiotherapy) or systemic treatment (chemotherapy, immunotherapy, any systemic investigational therapy, or EGFR-directed therapy) within 4 weeks before ASP-1929 PIT treatment. Note: Patients will be permitted to continue taking routine or necessary medications except for photosensitizing medications (see criterion 4 below). 2. History of significant (≥ Grade 3) infusion reaction to anti-EGFR antibodies.  3. History of allergic reactions attributed to compounds of similar chemical or biologic composition to ASP-1929, or other agents used in study. 4. Require use of photosensitizing medications (refer to Table 4 for list of common photosensitizing medications). Note: Photosensitizing medications must be discontinued 30 days before ASP-1929 PIT treatment. 5. Tumor invading major blood vessel unless the vessel has been embolized, stented, or surgically ligated to prevent hemorrhage; must not have involvement of the common or internal carotid arteries defined as invasion, encasement or direct contact (lack of a radiographically visible plane between the tumor and carotid artery). Decision to exclude will be determined by the Investigator. 6. Tumors inappropriate for PIT treatment, including those in the brain or dura, with perineural involvement at the skull base, CNS disease, or disease in the orbit (if the eye has been previously removed, consult with Medical Monitor before excluding). Decision to exclude will be determined by Investigator. 7. Present history of distant metastatic disease (M1). 8. Any contraindications for CT or 18FDG PET/CT imaging. 9. Weight > 350 pounds (weight limit for scanner table), or unable to fit within the imaging gantry. Requiring future examinations or treatments within 4 weeks after an ASP-1929 PIT treatment cycle exposing the patient to high-intensity light (eg, eye examinations, surgical procedures) that are unrelated to ASP-1929 PIT treatment, the disease under study, or the study overall. 11. Diagnosed and/or treated for additional malignancy within 3 years before study Day 1, except for those with a negligible risk of metastasis or death (such as adequately treated carcinoma in situ of the cervix, basal or squamous cell skin cancer, localized prostate cancer, or ductal carcinoma in situ). Patients with a history of other prior cancer treated with complete surgical resection and with no evidence of disease may be eligible based on discussion with the Medical Monitor. 12. Known history of testing positive for human immunodeficiency virus or acquired immunodeficiency syndrome -related illness. 13. Known infection or detection of active Hepatitis B (eg, HBsAg positive), Hepatitis C (eg, RNA [qualitative]), or SARS-CoV-2 (qualitative). 14. Received a live, attenuated vaccine within 4 weeks before Day 1 or anticipation of receiving a live, attenuated vaccine will be required during the study (based on known medical history). Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (eg, Flu-Mist®) are live attenuated vaccines, and are not allowed. 15. 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.  16. Major surgery or significant traumatic injury within 4 weeks of study Day 1, or anticipation of the need for major surgery that is unrelated to study intervention during the study. Note: If patient has had major surgery, they must have recovered adequately from the toxicity and/or complications before study Day 1. 17. Currently participating or participated in a study of any investigational agent or used any investigational device within 4 weeks of study Day 1. 18. Unwilling or unable to follow protocol requirements. 19. Any other condition which, in the Investigator's opinion, deems the patient an unsuitable candidate to receive ASP-1929 and/or be exposed to illumination, may affect the interpretation of the results, or render the patient at high risk from treatment complications