ASP-1929 Photoimmunotherapy (PIT) Study in Recurrent Head/Neck Cancer for Patients Who Have Failed at Least Two Lines of Therapy

Overall Inclusion Criteria: * Have a histologically confirmed locoregional persistent, recurrent or second primary squamous cell carcinoma of the head and neck, not amenable to curative treatment * Have failed or progressed on or after at least 2 lines of therapy for squamous cell carcinoma of the head and neck, one of which must be prior systemic platinum-based chemotherapy * Have completed prior curative radiation therapy for treatment of their head and neck region * Have locoregional head and neck tumor site(s) that are all accessible to light illumination * Have target tumors that are clearly measurable by contrast enhanced CT scan, or MRI scan with gadolinium if CT scan is not adequate or the patient has an allergy to CT contrast media. * Have a life expectancy of \> 6 months, based on Investigator judgment * Male participants must agree to use contraception during the treatment period and for at least 6 months after the last ASP-1929 infusion * Female patients of childbearing potential must not be pregnant or breastfeeding and agree to follow the contraceptive guidance during the treatment period and for at least 6 months after the last dose of trial intervention and must refrain from breastfeeding for at least 2 months after the last ASP-1929 infusion * Have an Eastern Cooperative Oncology Group (ECOG) score of 0 or 1 Overall Exclusion Criteria: * Have a history of significant (\>= Grade 3) cetuximab infusion reactions * Have been treated with prior systematic chemotherapy or targeted small molecule therapy or radiation therapy within 2 weeks of trial Day 1 or not recovered from adverse events due to a previously administered agent * Have been treated with an anticancer monoclonal antibody therapy within 4 weeks of trial Day 1 or have not recovered from adverse events due to previously administered agent * Have been treated with an investigational agent or intervention within 4 weeks of trial Day 1 or have not recovered from adverse events, due to previously administered agent or intervention * Have a present history of distant metastatic disease (M1) * Have an active undergoing treatment or have a diagnosis of an active cancer other than nonmelanoma skin cancer or HNSCC * Have a tumor in enhanced CT or MRI scan invading a major blood vessel, unless the vessel has been embolized, stented or surgically ligated to prevent potential bleeding from a blood vessel * Have impaired hepatic function * Have impaired renal function * Have 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 trial requirements * Have been previously treated or randomized to any trial using ASP-1929 or RM-1929 PIT as the study treatment