Second-line Therapy for Patients With Progressive Poorly Differentiated Extra-pulmonary Neuroendocrine Carcinoma

Inclusion Criteria: 1. Age ≥18 years and life expectancy ≥3 months. 2. Diagnosed with poorly differentiated (as defined by the World Health Organisation in 2010, Ki 67 ≥20%) extra-pulmonary neuroendocrine carcinoma (NEC grade 3, confirmed by histology). (Carcinoma of unknown primary is allowed if lung primary has been excluded following review by the multi-disciplinary team). 3. Prior treatment with first-line platinum-based chemotherapy for NEC in the advanced setting and ≥28 days from Day 1 of the previous treatment cycle. 4. Documented radiological evidence of disease progression OR discontinuation of first-line platinum-based chemotherapy due to intolerance. 5. Measurable disease according to RECIST 1.1 6. Eastern Co-operative Oncology Group (ECOG) performance status ≤2 7. Adequate renal function with serum creatinine ≤1.5 times upper limit of normal (ULN) and creatinine clearance ≥50ml30ml/min according to Cockroft-Gault or Wright formula. If the calculated creatinine clearance is less than 30 ml/min, glomerular filtration rate (GFR) may be assessed using either Cr51-EDTA or 99mTc-DTPA clearance method to confirm if GFR is ≥30 ml/min). 8. Adequate haematological function: Hb ≥90g/L, WBC ≥3.0 x 109/L, ANC ≥1.5 x 109/L, platelet count ≥100 x 109/L. 9. Adequate liver function: serum total bilirubin 1.5 x ULN (biliary drainage is allowed for biliary obstruction) and ALT and/or AST 2.5 x ULN in the absence of liver metastases, or 5 x ULN in the presence of liver metastases. 10. A negative pregnancy test is required at registration in women of childbearing potential. 11. Men and women of reproductive potential must agree to use a highly effective form of contraception during the study and for 6 months following the last dose of trial treatment. In addition, male participants should use a condom during study participation and for 6 months following the last dose of trial treatment. 12. Patients must be able to provide written informed consent. 13. Patients must be able and willing to comply with the terms of the protocol. Exclusion Criteria: 1. Known or suspected allergy or hypersensitivity reaction to any of the components of study treatment or their excipients. 2. Use (including self-medication) within one week of randomisation and for the duration of the study of any of the following: St. John's wort, grapefruit, Seville oranges, medicines known to inhibit UGT1A1 (e.g. atazanavir, gemfibrozil, indinavir) and medicines known to inhibit or induce either CYP3A4 or CYP3A5 3. Previous treatment (for neuroendocrine carcinoma) with any of the components of combination chemotherapy regimens detailed in this study (nal-IRI or 5-FU or irinotecan or topoisomerase inhibitors or taxane-based therapy). 4. Incomplete recovery from previous therapy in the opinion of the investigator (surgery/adjuvant therapy/radiotherapy/chemotherapy in advanced setting), including ongoing peripheral neuropathy of Common Terminology Criteria for Adverse Events (CTCAE) grade 2 from previous platinum-based therapy. 5. Concurrent palliative radiotherapy involving target lesions used for this study (\<28 days from discontinuation of radiotherapy). Radiotherapy for non-target lesions is allowed if other target lesions are available outside the involved field. 6. Patients must not have a history of other malignant diseases (within the previous 3 years, and there must be no evidence of recurrence), other than: * Extra-pulmonary neuroendocrine carcinoma. * Non-melanoma skin cancer where treatment consisted of resection only or radiotherapy. * Ductal carcinoma in situ (DCIS) where treatment consisted of resection only. * Cervical carcinoma in situ where treatment consisted of resection only. * Superficial bladder carcinoma where treatment consisted of resection only. 7. Documented brain metastases, unless adequately treated (surgery or radiotherapy only), with no evidence of progression and neurologically stable off anticonvulsants and steroids. 8. Clinically significant gastrointestinal disorder (in the opinion of the treating clinician) including hepatic disorders, bleeding, inflammation, obstruction, or diarrhoea ≥CTCAE grade 1 (at time of study entry). 9. Severe arterial thromboembolic events (myocardial infarction, unstable angina pectoris, stroke) less than 6 months before inclusion. 10. New York Heart Association (NYHA) Class III or IV congestive heart failure, ventricular arrhythmias or uncontrolled blood pressure . 11. Severe bone marrow failure or bone marrow depression after radiotherapy or treatment with other antineoplastic agents (defined as haematological values of haemoglobin or white blood cells or neutrophils or platelets not meeting inclusion criteria). 12. Known active hepatitis B virus, hepatitis C virus or HIV infection. 13. Active chronic inflammatory bowel disease. 14. Breastfeeding women. 15. Evidence of severe or uncontrolled systemic diseases which, in the view of the treating clinician, makes it undesirable for the patient to participate in the trial. 16. Evidence of significant clinical disorder or laboratory finding which, in the opinion of the treating clinician, makes it undesirable for the patient to participate in the trial. 17. Medical or psychiatric conditions that impair the ability to give informed consent. 18. Any other serious uncontrolled medical conditions (in the opinion of the treating clinician).