A Study of Etoposide-carboplatin in Combination With Pembrolizumab and Lenvatinib Maintenance in HG-NETs

Inclusion Criteria: In order to be eligible for participation in this trial, the participant must: 1. Be willing and able to provide written informed consent for the trial. 2. Be 18 years or above of age on day of signing informed consent. 3. ECOG performance status of 0-2. 4. Have histologically or cytologically confirmed diagnosis of poorly differentiated neuroendocrine carcinoma. 5. Have Ki-67 labelling index \>20% and/or \>20 mitoses/10 high-power fields. 6. Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. 7. Have had no prior systemic treatment in the metastatic setting. 8. Demonstrate adequate organ function. 9. Female subject of childbearing potential should have a negative urine or serum pregnancy. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. 10. Women of childbearing potential must be willing to use a highly effective method of contraception for the course of the study through 120 days after the last dose of Investigational Medicinal Product (IMP). Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. 11. Sexually active males must agree to use an adequate method of contraception starting with the first dose of IMP through 120 days after the last dose of study therapy. Note: Abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject. Exclusion Criteria: The participant must be excluded from participating in the trial if the participant: 1. Has a diagnosis of large cell and small cell histology of lung origin or Merkel cell carcinoma. 2. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. 3. Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease and stereotactic radiotherapy to the CNS. 4. Has an active infection requiring systemic therapy. 5. Has a known history of Human Immunodeficiency Virus (HIV). Note: No HIV testing is required unless mandated by local health authority. 6. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA detectable levels) infection. Note: no testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. 7. Has a known history of active Bacillus Tuberculosis (TB). 8. Has a known history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 9. Has a known history of interstitial of lung disease. 10. Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. 11. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 12. Uncontrolled blood pressure (Systolic BP\>140 mmHg or diastolic BP \>90 mmHg) in spite of an optimized regimen of antihypertensive medication. 13. Significant cardiovascular impairment: history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or stroke within 6 months of the first dose of study drug. 14. Bleeding or thrombotic disorders or subjects at risk for severe haemorrhage. The degree of tumour invasion/infiltration of major blood vessels (e.g. carotid artery) should be considered because of the potential risk of severe haemorrhage associated with tumour shrinkage/necrosis following lenvatinib therapy. 15. Subjects having \>1+ proteinuria on urine dipstick testing unless a 24-hour urine collection for quantitative assessment indicates that the urine protein is \<1 g/24 hours. 16. Is currently participating and receiving therapy or has participated or is participating in a study of an IMP or used an investigational device within 4 weeks of the first dose of IMP. 17. Has had major surgery within 3 weeks prior to first dose of study treatment. 18. Has a history of hypersensitivity to pembrolizumab, lenvatinib, carboplatin, etoposide or any of their excipients. 19. Has a known history of an additional malignancy, except if the participant has undergone potentially curative therapy with no evidence of that disease recurrence for ≥3 years since initiation of that therapy. (Note: The time requirement does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, superficial bladder cancer, squamous cell carcinoma of the skin, in situ cervical cancer, or other in situ cancers.). 20. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating Principal Investigator (PI). 21. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 22. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through to 120 days after the last dose of IMP. 23. Has received prior therapy with an anti-PD-1, anti-PD-L1 or anti-PD-L2 agent. 24. Has received a live vaccine within 30 days of first dose of IMP administration. Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist®) are live attenuated vaccines, and are not allowed.