Single cEll pRofiling PErsistaNce To ImmuNothErapy

Inclusion Criteria: * 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. 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. 2. 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: 1. Hemoglobin ≥9.0 g/dL 2. Absolute neutrophil count (ANC) 1.5 (or 1.0) x 109/L (\> 1500 per mm3) 3. Platelet count ≥100 x 109/L (\>75,000 per mm3) 4. 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. 5. 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 6. 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. 7. 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: 1. 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). 2. 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. Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigation device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 14 days prior to the first dose of trial treatment. The following are exceptions to this criterion: 1. Intranasal, inhaled, topical steroids, or local steroid injections (e.g., intra articular injection) 2. Systemic corticosteroids at physiologic doses not to exceed \<\<10 mg/day\>\> of prednisone or its equivalent 3. Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication). * Has had a prior anti-cancer mAb within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from AEs due to mAbs administered more than 4 weeks earlier. * Has had prior chemotherapy, targeted small molecule therapy, hormonal therapy or radiation therapy for cancer therapy within 2 weeks prior to study Day 1. Concurrent use of hormonal therapy for non-cancer-related conditions (e.g., hormone replacement therapy) is acceptable. * Any unresolved toxicity NCI CTCAE Grade ≥2 from previous anticancer therapy with the exception of alopecia, vitiligo, and the laboratory values defined in the inclusion criteria: 1. Patients with Grade ≥2 neuropathy will be evaluated on a case-by-case basis after consultation with the Study Physician. 2. Patients with irreversible toxicity not reasonably expected to be exacerbated by treatment with durvalumab may be included only after consultation with the Study Physician. * Major surgical procedure (as defined by the Investigator) within 28 days prior to the first dose of study drug and patients must have recovered adequately from the eventual toxicity and/or complications related with the surgical procedure. Note: Local surgery of isolated lesions for palliative intent is acceptable. * Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. * History of allogenic organ transplantation. * Has known active CNS metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least 4 weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. * Active or prior documented autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., colitis or Crohn's disease\], diverticulitis \[with the exception of diverticulosis\], systemic lupus erythematosus, Sarcoidosis syndrome, or Wegener syndrome \[granulomatosis with polyangiitis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.\]). The following are exceptions to this criterion: 1. Patients with vitiligo or alopecia 2. Patients with hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement 3. Any chronic skin condition that does not require systemic therapy 4. Patients without active disease in the last 5 years may be included but only after consultation with the study physician 5. Patients with celiac disease controlled by diet alone. * Has evidence of interstitial lung disease or a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Has an active infection requiring systemic therapy, also including tuberculosis (clinical evaluation that includes clinical history, physical examination and radiographic findings, and TB testing in line with local practice), hepatitis B (known positive HBV surface antigen (HBsAg) result), hepatitis C. Patients with a past or resolved HBV infection (defined as the presence of hepatitis B core antibody \[anti-HBc\] and absence of HBsAg) are eligible. Patients positive for hepatitis C (HCV) antibody are eligible only if polymerase chain reaction is negative for HCV RNA. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * 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 investigator. The conditions also include uncontrolled intercurrent illness, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, interstitial lung disease, serious chronic gastrointestinal conditions associated with diarrhea, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs or compromise the ability of the patient to give written informed consent. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the trial, starting with the screening visit through 120 days after the last dose of trial treatment. * Has previously received prior therapy with an anti-PD-1, anti-PD-L1 including durvalumab, or anti CTLA-4 (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways). * Has received a live vaccine within 30 days of planned start of study therapy. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. * Judgment by the investigator that the patient is unsuitable to participate in the study and the patient is unlikely to comply with study procedures, restrictions, and requirements.