Avelumab in G3 NEC

Inclusion Criteria: * Adults (males or females), aged 18 years or older with pathologically confirmed, advanced (unresectable or metastatic) neuroendocrine tumour from a gastroenteropancreatic or lung source. Both participants with functional NETs and those with nonfunctional NETs shall be eligible for this study. * Histologically confirmed, WHO Grade 3, poorly-differentiated NEC. * Has received 0,1 or 2 prior lines of systemic therapy (chemotherapy, PRRT, targeted therapies such as everolimus or sunitinib). Somatostatin analogues are not considered a line of therapy for the purposes of this criterion. * Radiological documentation of disease progression within 24 weeks of study enrolment. Disease progression must be demonstrated on two scans less than one year apart. * Participants previously treated with any systemic therapies are eligible to enroll if disease progression is documented during or after their last treatment. * Measurable disease as assessed by CT scan of the chest, abdomen and pelvis which is suitable for accurate repeated measurements (according to RECIST v1.1). * ECOG performance status 0-2. * Adequate bone marrow function (ANC \> 1.5 x 109/L; Platelets \>100 x109/L; haemoglobin \> 90 g /L). * Adequate liver function defined by a total bilirubin level ≤1.5xULN and AST and ALT levels ≤2.5xULN for participants (or AST and ALT levels ≤ 5xULN for participants with documented metastatic disease to the liver). * Adequate renal function defined by an estimated creatinine clearance ≥ 30 mL/min according to the Cockcroft-Gault formula (or local institutional standard method). * Willing and able to comply with all study requirements, including timing and/or nature of treatment and required assessments. * Signed, written informed consent. * Evidence of post-menopausal status, or negative urine or serum pregnancy test for female pre-menopausal participants (within approximately 14 days prior to enrolment). Women will be considered post-menopausal if they have been amenorrhoeic for 12 months without an alternative medical explanation. * Highly effective contraception for both male and female participants if the risk of conception exists (note: The effects of the IP on the developing human fetus are unknown; thus, women of childbearing potential and men able to father a child must agree to use 2 highly effective contraceptions, defined as methods with a failure rate of less than 1% per year. Highly effective contraception is required at least 28 days prior, throughout and for at least 60 days after avelumab treatment.) Exclusion Criteria: * Grade 1-2 NET, or Grade 3 well-differentiated neuroendocrine tumour, or mixed adenoneuroendocrine carcinomas (MANEC) * NETs confirmed to be from a primary other than the gastrointestinal tract, pancreas or lung. * Prior use of PD-1, PD-L1 or CTLA-4 inhibitors * Life expectancy of ≤3 months * Concurrent treatment with other anticancer therapy (except somatostatin analogues for the purposes of functional control). Participants on somatostatin analogues for anti-proliferative therapy should have this therapy ceased, and would be eligible for enrolment if they have not received somatostatin analogues in the past 14 days. * Active autoimmune disease that might deteriorate when receiving an immunostimulatory agent, with exception to: * Subjects with diabetes type I, vitiligo, psoriasis, hypo- or hyperthyroid disease not requiring immunosuppressive treatment are eligible * Active infection requiring systemic therapy. * History of primary autoimmunodeficiency * Current use of immunosuppressive medication, EXCEPT for the following: a. intranasal, inhaled, topical steroids, or local steroid injection (e.g., intra-articular injection); b. Systemic corticosteroids at physiologic doses ≤ 10 mg/day of prednisone or equivalent; c. Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication) * Prior organ transplantation, including allogeneic stem cell transplantation * Clinically significant (i.e., active) cardiovascular disease: cerebral vascular accident/stroke (\< 6 months prior to enrollment), myocardial infarction (\< 6 months prior to enrollment), unstable angina, congestive heart failure (≥ New York Heart Association Classification Class II), or serious cardiac arrhythmia requiring medication. * Major surgery in the 2 weeks prior to randomization. Surgery with intent to debulk metastatic disease is allowed, as long as there is sufficient residual disease for RECIST measurements (see inclusion criteria 5). * Participants with prior or concurrent malignancy except for the following: adequately treated basal cell or squamous cell skin cancer, or other adequately treated in situ cancer, or any other cancer from which the patient has been disease free for three years. * All participants with brain metastases and any of the following: * They have not received local treatment to known brain metastases * They have been clinically unstable in the 2 weeks prior to enrolment * Requirement for treatment with systemic steroids exceeding the equivalent of 10mg oral prednisone per day * Ongoing neurological symptoms related to brain metastases * Leptomeningeal metastases * Pregnancy, lactation, or inadequate contraception. * Significant acute or chronic infections including, among others: * Known history of positive test for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Positive test for HBV surface antigen and / or confirmatory HCV RNA (if anti-HCV antibody tested positive) * Active tuberculosis * Testing for these diseases is not mandatory unless clinically indicated. * Known prior severe hypersensitivity to investigational product or any component in its formulations, including known severe hypersensitivity reactions to monoclonal antibodies (NCI CTCAE v4.03 Grade ≥ 3) * Persisting toxicity related to prior therapy of Grade \>1 NCI-CTCAE v 4.03; however, alopecia, sensory neuropathy Grade ≤ 2, or other Grade ≤ 2 not constituting a safety risk based on investigator's judgment are acceptable. * Known alcohol or drug abuse * Other severe acute or chronic medical conditions including colitis, inflammatory bowel disease, pneumonitis, pulmonary fibrosis or psychiatric conditions including recent (within the past year) or active suicidal ideation or behavior; or laboratory abnormalities that may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and, in the judgment of the investigator, would make the patient inappropriate for entry into this study. * Any psychiatric condition that would prohibit the understanding or rendering of informed consent * Vaccination within 4 weeks of the first dose of avelumab and while on trial, except for administration of inactivated vaccines * Inability to obtain sufficient tumour tissue (whether archival or fresh) for PD-L1 testing. A core biopsy, endoscopic biopsy or surgical resection specimen shall be considered adequate tissue; a fine needle aspirate/biopsy will be considered insufficient tissue. * Prior treatment for study indication with: * Peptide Receptor Radiouclide Therapy (PRRT) administered within 3 months of enrolment * Hepatic intra-arterial embolization, radio-frequency ablation, or cryoablation within 4 weeks of enrolment