• Capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in this protocol. Written informed consent and any locally required authorization (e.g., Health Insurance Portability and Accountability Act in the US, European Union \[EU\] Data Privacy Directive in the EU) obtained from the patient/legal representative prior to performing any protocol-related procedures, including screening evaluations.

• Age \> 18 years at time of study entry.

• Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

‣ Cohort 1: histologically confirmed recurrent or metastatic CRC or endometrial cancer irrespective of prior treatment history with chemotherapy and/or targeted agents, not amenable to surgery and known tumor MSI-H or dMMR status per local standard of practice.

⁃ Cohort 2: histologically confirmed recurrent or metastatic CRC not amenable to surgery and known tumor MSS or pMMR status per local standard of practice, that have progressed during or after, at least 2 lines of fluoropyrimidine, irinotecan and/or oxaliplatin containing therapy with or without bevacizumab according to institutional practice or have not tolerated therapy for advanced/metastatic disease; if epidermal growth factor receptor (EGFR) positive/RAS wild type, prior anti-EGFR treatment is required. Or histologically confirmed recurrent or metastatic endometrial cancer that have progressed during or after a platinum and taxane-based regimen, not amenable to surgery and known tumor MSS or pMMR status per local standard of practice.

• Life expectancy of \> 12 weeks.

• Body weight \>30 kg.

• Adequate normal organ and marrow function as defined below:

‣ Hemoglobin ≥9.0 g/dL

⁃ Absolute neutrophil count (ANC) 1.5 (or 1.0) x 109/L (\> 1500 per mm3)

⁃ Platelet count ≥100 x 109/L (\>75,000 per mm3)

⁃ Serum bilirubin ≤1.5 x institutional upper limit of normal (ULN). This will not apply to patients with confirmed Gilbert's syndrome (persistent or recurrent hyperbilirubinemia that is predominantly unconjugated in the absence of hemolysis or hepatic pathology), who will be allowed only in consultation with their physician.

⁃ AST (SGOT)/ALT (SGPT) ≤2.5 x institutional upper limit of normal unless liver metastases are present, in which case it must be ≤5 x ULN

⁃ Measured creatinine clearance (CL) \>40 mL/min or Calculated creatinine CL\>40 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance.

⁃ Creatinine ≤1.5 x ULN OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCla) ≥60 mL/min for subject with creatinine levels \>1.5 x institutional ULN. Creatinine clearance (CrCl) should be calculated per institutional standard.

• Evidence of post-menopausal status or negative urinary or serum pregnancy test for female pre-menopausal patients. Women will be considered post-menopausal if they have been amenorrheic for 12 months without an alternative medical cause. The following age-specific requirements apply:

‣ Women \<50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of exogenous hormonal treatments and if they have luteinizing hormone and follicle-stimulating hormone levels in the post-menopausal range for the institution or underwent surgical sterilization (bilateral oophorectomy or hysterectomy).

⁃ Women ≥50 years of age would be considered post-menopausal if they have been amenorrheic for 12 months or more following cessation of all exogenous hormonal treatments, had radiation-induced menopause with last menses \>1 year ago, had chemotherapy-induced menopause with last menses \>1 year ago, or underwent surgical sterilization (bilateral oophorectomy, bilateral salpingectomy, or hysterectomy).

• Patient is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up.

• Have at least 1 tumoral lesion of minimum 10 mm in diameter that is suitable for initial biopsy.

• Presence of at least 1 measurable lesion according to RECIST v1.1 apart from the lesion that is biopsiable before initiating treatment.

• Male and Female subjects of childbearing potential must be willing to use an adequate method of contraception as outlined in Section 7.1 for the course of the trial and for 180 days after the last dose of durvalumab + tremelimumab combination therapy or 90 days after the last dose of durvalumab monotherapy, whichever is the longer time period.