-INCLUSION CRITERIA:  Histologically or cytologically confirmed recurrent or metastatic ONB not amenable to potentially curative local therapies. Review of tissue samples by Pathology at the NIH is preferred. Participants must have measurable disease, per RECIST 1.1. A previously treated lesion by radiotherapy can be chosen as the target lesion only if progression in the respective lesion has been demonstrated during or following radiotherapy. Participants should have received at least one line of systemic therapy including a platinum agent, with evidence of disease progression clinically or radiographically. Men or Women >=18 years of age on day of signing informed consent. Because no dosing or adverse event data are currently available on the use of bintrafusp alfa in participants <18 years of age, children are excluded from this study. ECOG performance status (PS) =<2.  Participants must have adequate organ and marrow function as defined below:  Absolute neutrophil count (ANC) >=1,500/mcL Hemoglobin<TAB>>=9 g/dL (transfusions allowed) Platelets >=100,000/mcL Serum Creatinine <= 1.5 (SqrRoot) ULN OR Measured CrCl or eGFR by CKD- EPI formula may be used to estimate CrCl/eGFR >=30 mL/min/1.73m^2 for participant with creatinine levels > 1.5 x institutional ULN Serum total bilirubin <=1.5 x upper limit of normal (ULN) OR Direct bilirubin <=ULN for participants with total bilirubin levels >1.5 x ULN AST(SGOT) and ALT(SGPT) <=2.5 (SqrRoot) ULN  The effects of immunotherapy on the developing human fetus are unknown. Therefore, participants must use effective methods of contraception (such as implants, injectables, combined oral contraceptives, IUDs, sexual abstinence or vasectomized partner).  Women of child-bearing potential (WOCBP: any woman who has experienced menarche and has not had hysterectomy or bilateral oophorectomy or is not postmenopausal (amenorrheic 12 months or more following cessation of exogenous hormonal treatments; if <50 years old need follicle stimulating hormone FSH in the post-menopausal range)) must agree to use highly effective contraception prior to study entry and for up to 65 days following the last dose of study treatment. Men must agree to use highly effective contraception prior to study entry and up to 125 days following the last dose of study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Participants with bone metastases or hypercalcemia on intravenous bisphosphonate treatment, zolendronic acid, denosumab, or similar agents are eligible to participate and may continue this treatment. Participants with treated CNS ONB lesions are eligible if follow-up brain imaging after at least a month following central nervous system (CNS)-directed therapy shows no evidence of progression. Participants with new or progressive non-intraparenchymal CNS ONB lesions are eligible if the treating physician determines that immediate CNS specific treatment is not required and is unlikely to be required during the first cycle of therapy. Human immunodeficiency virus (HIV)-positive participants must have CD4 count >= 200 cells per cubic millimeter at enrollment, be on stable antiretroviral therapy for at least 4 weeks and have no reported opportunistic infections or Castleman s disease within 12 months prior to enrollment. For participants with serological evidence of chronic hepatitis B virus (HBV) infection, the HBV DNA viral load must be undetectable on suppressive therapy, if indicated. For participants with serological evidence of HCV infection, the HCV RNA viral load must be negative to be eligible for study participation. Ability of participant to understand and the willingness to sign a written informed consent document.  Must co-enroll in the following two studies. A separate inform consent will be obtained from participant for these studies.  21-C-0009: A Natural History Study of Children and Adults with Olfactory Neuroblastoma, and 18-DC-0051: Biospecimen procurement for NIDCD clinical protocols  EXCLUSION CRITERIA:  Anticancer treatment, concurrent or prior (chemotherapy, monoclonal antibody, cytokine therapy, immune therapy, targeted small molecule therapy) or any investigational drug, within 4 weeks or 5 half-lives (whichever shorter) prior to the first drug administration. All residual treatment-related toxicities must have resolved or be minimal and not constitute a safety risk. Note: Palliative radiotherapy is permitted concurrently or within the pretreatment period. Subjects receiving bisphosphonates or denosumab are eligible provided treatment was initiated at least 14 days before treatment. Participants who received prior checkpoint blockade therapy and were taken off treatment for serious adverse events related to immuno-therapy are excluded. Major surgery within 4 weeks prior to the first drug administration (minimally invasive procedures such as diagnostic biopsies are permitted).  Active or prior documented autoimmune or inflammatory diseases that might deteriorate on immunostimulatory agent (including colitis or Crohn s disease, systemic lupus erythematosus, sarcoidosis, vasculitis, Grave s disease, hypophysitis, uveitis, rheumatoid arthritis etc.), except the following:  Type I diabetes mellitus Chronic skin conditions that do not require systemic therapy (including eczema, vitiligo, alopecia, psoriasis) Hypothyroidism (e.g. post-Hashimoto thyroiditis) stable, on hormone replacement Mild autoimmune disease not active in the last 5 years may be eligible after consultation with the principal investigator.  Current use of immunosuppressive medication within 14 days before the first dose of the study medication, except the following:  Intranasal, inhaled, topical glucocorticoids; locally injected glucocorticoids (i.e. intra-articular, intra-ocular) Systemic glucocorticoids at physiologic doses (generally <= 10 mg prednisone or equivalent per day) Glucocorticoids as premedication for contrast-enhanced studies is allowed prior to enrollment and on study.  Uncontrolled intercurrent chronic or acute illness including, but not limited to the following, that may limit interpretation of results or increase risk to the participant in the judgment of the investigator:  Bleeding diathesis or recent (<3 months) clinically significant bleeding event. Prior organ transplantation including allogenic stem-cell transplantation  Impaired cardiovascular function or clinically significant cardiovascular disease, including, but not limited to, any of the following:  cerebral vascular accident/stroke (< 3 months prior to enrollment), acute coronary syndromes (including myocardial infarction < 6 months prior to enrollment, unstable angina), congestive heart failure (>= New York Heart Association Classification Class III), left ventricular ejection fraction (LVEF) <= 50% determined by transthoracic echocardiogram (TTE) or multi-gated acquisition scan (MUGA), history or presence of clinically significant cardiac arrhythmia including resting bradycardia, uncontrolled atrial fibrillation or paroxysmal supraventricular tachycardia (controlled arrhythmias, e.g. stable atrial fibrillation, may be allowed at the discretion of the investigator), history of myocarditis History of idiopathic pulmonary fibrosis, drug-induced or idiopathic pneumonitis, active interstitial lung disease, blood oxygen saturation <90% at rest (on ambient air). Clinically significant hepatic disease. Active infection requiring systemic therapy (minor infections may be allowed at the discretion of the investigator). Subjects unwilling to accept blood products as medically indicated. Vaccination with live vaccines within 4 weeks of the first dose of treatment and while on study is prohibited. Inactivated vaccines may be administered. History of allergic reactions or hypersensitivity attributed to compounds of similar chemical or biologic composition to bintrafusp alfa. Participants with history of severe hypersensitivity reaction to monoclonal antibodies (grade >= 3 NCI-CTCAE v5) will be evaluated by the allergy/immunology team prior to enrollment. History of second malignancy within 3 years of enrollment except for the following: adequately treated localized basal cell or squamous skin cancer, cervical carcinoma in situ, superficial bladder cancer, other localized malignancy which has been adequately treated or malignancy which does not require active systemic treatment (e.g. low risk CLL). Pregnant or breastfeeding women are excluded from this study because the study medications have not been tested in pregnant women and there is potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study medications, breastfeeding should be discontinued if the mother is treated on this protocol.