EMITT-1 (ERAP Mediated Immunopeptidome Targeting Trial - 1)

Inclusion Criteria: 1. Provision of written informed consent. 2. Male or female, ≥ 18 years of age. 3. An ECOG performance status of 0 or 1. 4. Willing to permit access to stored historical tumour tissue and prior tumour radiological assessments and tumour biomarker data (if available). 5. Able to take oral medications and be willing to record daily adherence to the study drug. 6. Female participants must be of non-child-bearing potential, or, if of childbearing potential must have a negative pregnancy test (as required by protocol), must use a highly effective method of contraception combined with a condom and not donate ova (for the protocol specified period of time). 7. Male participants must use a condom and their female participant must also use a highly effective method of contraception (for the protocol specified period of time), if engaging in sexual intercourse with a female partner who could become pregnant and not donate sperm. 8. Estimated life expectancy of at least 3 months, in the opinion of the PI. 9. Willing and able to comply with all scheduled visits, treatment plans, laboratory tests, and other study procedures. 10. Participant has measurable disease per RECIST 1.1/iRECIST 11. Participant has cytologically or histologically confirmed locally advanced or metastatic solid malignancy for which no further standard of care (SoC) therapy is available (or no SoC therapy exists), or who have been offered and declined SoC therapy, or are intolerant of SoC therapy. Module 1 (Part B) and Module 2 (Part B) Only 12. Participant has at least one tumour lesion amenable to serial biopsies and is willing to provide consent for biopsies and has measurable disease per RECIST 1.1/iRECIST, excluding the lesion(s) identified for biopsy. Module 2 (Part C and Part D) Cohort 1 (Cervical) 13. Participants with histologically confirmed persistent, recurrent or metastatic cervical cancer who are not amenable to curative therapy. 14. Participants should have received at least 3 months first line anti-PD(L)-1 therapy (± bevacizumab, chemotherapy, ADC or other immunotherapy e.g. anti-CTLA-4) and this should have included at least a 10-week period without progression. 15. Participants may enrol in the study immediately following progression on the first line CPI or may have received 1 further line of systemic cancer therapy after progression on CPI. Cohort 2 (Hepatocellular Carcinoma) 16. Participants with histologically confirmed hepatocellular carcinoma who are not amenable to curative therapy and ineligible for loco-regional therapy. 17. Participants should have received at least 3 months first line anti-PD(L)-1 containing therapy and this should have included at least a 10-week period without progression per Investigator assessment. 18. Participants may enrol in the study immediately following progression on the first line CPI or may have received 1 further line of systemic cancer therapy after progression on CPI. 19. Participant has Child-Pugh score class A liver function. Cohort 3 (Moderate to High TMB) 20. Participants with cytologically or histologically confirmed advanced, recurrent or metastatic disease, which is not amenable to curative therapy, in up to 5 types of solid tumour with moderate to high median TMB (NSCLC, urothelial, SCCHN, gastric/gastro-oesophageal adenocarcinoma, oesophageal SCC). 21. Participants should have received at least ≥ 3 months first line anti-PD(L)-1 (± chemotherapy, ADC, pemetrexed or other immunotherapy e.g. anti-CTLA-4) and this should have included at least a 10-week period without progression. 22. Participants may enrol in the study immediately following progression on the first line CPI or may have received 1 further line of systemic cancer therapy after progression on CPI. Module 2 Part D only (pMMR/MSS-CRC) 23. Participants with histologically confirmed unresectable pMMR/MSS-CRC, without current or prior liver metastases 24. Participants should have received at least one line of therapy in the advanced/metastatic setting and should have received therapies according to local standard practice, unless ineligible or intolerant to the treatment 25. Participants may not have received more than 2 lines of cytotoxic chemotherapy Exclusion Criteria: 1. Prior therapy with an ERAP1 inhibitor. 2. Any other malignancy within the past 3 years, with the exception of cervical intraepithelial neoplasia and nonmelanoma skin cancer. 3. Any unresolved toxicity (except alopecia) from prior therapy of ≥ CTCAE Grade 1. Participants with Grade 2 toxicity that is not clinically significant (e.g., alopecia, vitiligo), or that is deemed stable or irreversible (e.g., peripheral neuropathy) can be enrolled. 4. Active or documented history of autoimmune disease (within 2 years) requiring systemic immunosuppressive therapy, or participant is immunocompromised for any other reason (as determined by the Investigator). 5. Spinal cord compression or brain metastases, unless asymptomatic, stable, and not requiring steroids for at least 4 weeks (if stable and requiring no intervention, the participant can be enrolled in the study). 6. Uncontrolled seizures. 7. Active infection requiring therapy within 14 days prior to the day of first dose of IMP. 8. Severe or uncontrolled medical condition (e.g., severe chronic obstructive pulmonary disease, severe Parkinson's disease, active inflammatory bowel disease) or psychiatric condition. 9. Active bleeding diatheses. 10. Participant has received an organ transplant. 11. Known active hepatitis B, hepatitis C, or human immunodeficiency virus infection (HIV). 12. Participant is breastfeeding or pregnant. 13. Receipt of licenced or unlicenced cytotoxic, noncytotoxic or small molecule treatment for the malignancy within 28 days or 5 half-lives, whichever is shorter prior to the day of first dose of IMP. 14. Receipt of oral corticosteroids (at a dose \> 10 mg prednisone/day or equivalent) within 14 days (except for subjects receiving corticosteroids for adrenal insufficiency). 15. Receipt of St John's Wort or of another concomitant medication, herbal supplement, or food that is a strong inhibitor or inducer of CYP3A4 enzymes within 14 days. 16. Receipt of a blood transfusion (blood or blood products) within 7 days. 17. Impaired hepatic or renal function. 18. Liver function deteriorating in a manner that would likely make the participant ineligible per protocol specified requirements. 19. Other evidence of impaired hepatic synthesis function. 20. Inadequate bone marrow reserve or organ function. 21. Any prior history of persistent (\> 4 weeks) severe pancytopenia due to previous therapy rather than to disease (ANC \< 0.5 × 10\^9/L or platelets \< 50 x 10\^9/L). 22. Cardiac dysfunction or other clinically significant cardiac pathology likely to impair the participants ability to participate in the study. 23. Mean QTcF \> 450 ms for males or \> 470 ms for females. 24. Any clinically important abnormalities in rhythm, conduction, or morphology on resting ECG. Controlled atrial fibrillation is permitted. 25. Any factor that in the Investigator's opinion increases the risk of QTc prolongation or arrythmic events. 26. In the opinion of the Investigator, unlikely to comply with study procedures, restrictions, or requirements. 27. A history of haemolytic anaemia or marrow aplasia. 28. Has received a live-virus vaccination within 28 days. Note: seasonal flu or COVID vaccines that do not contain live virus are permitted. 29. History of Grade 3 or 4 pneumonitis or interstitial lung disease within the last 5 years, or other clinically significant pulmonary pathology likely to impair ability to participate in the study. Module 2 all Parts and Module 1A Crossover Participants Only 30. Has discontinued a prior checkpoint inhibitor due to toxicity. 31. Hypersensitivity to cemiplimab or any of its excipients, or contraindicated to cemiplimab per approved local labelling. 32. Has experienced ≥ Grade 2 immune-mediated AE on this study (applies to crossover participants only). Module 2 Part D only - pMMR/MSS CRC dose optimisation cohort 33. Participants with unresectable pMMR/MSS CRC may not have purely peritoneal disease 34. Participants with unresectable pMMR/MSS CRC may not have had prior CPI / immunotherapy