Inclusion Criteria:

          1. Relapsed/refractory solid tumor patients not previously treated with anti-PD-1/PD-L1
             or anti-CTLA-4 immunotherapy whose tumors expressed a high tumor mutational burden
             (TMB) (TMB high >20 mutations/MB) or moderate TMB (10-20 mutations/MB) as based on
             next generation sequencing (NGS)

          2. Age >18 years at time of study entry

          3. Eastern Cooperative Oncology Group (ECOG) performance status of at least 2 and life
             expectancy greater than 3 months

          4. Accurate documentation of date of starting previous therapy and date of progression to
             establish TTP from most recent therapy

          5. Patient must have normal organ and marrow function independent of transfusion for at
             least 7 days prior to screening and independent of growth factor support for at least
             14 days prior to screening as defined below:

          6. Absolute neutrophil count (ANC ≥1.5 (or 1.0) x (> 1500 per mm3)

          7. Platelet count ≥100 (or 75) x 109/L (>75,000 per mm3)

          8. Serum bilirubin ≤1.5 x institutional upper limit of normal (ULN). This will not apply
             to patients with confirmed Gilbert's syndrome, who will be allowed only in
             consultation with their physician.

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

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

         11. The effects of MEDI4736 and tremelimumab on the developing human fetus are unknown.
             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:

         12. 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)

         13. 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)

         14. Females of childbearing potential who are sexually active with a non-sterilized male
             partner must use at least 1 highly effective method of contraception from the time of
             screening and must agree to continue using such precaution for 180 days after the last
             dose of durvalumab + tremelimumab combination therapy or 90 days after the last dose
             of durvalumab monotherapy. Non-sterilized male partners of female patient must use
             male condom plus spermicide throughout this period. Cessation of birth control after
             this point should be discussed with a responsible physician. Not engaging in sexual
             activity for the total duration of the drug treatment and the drug washout period is
             an acceptable practice; however, periodic abstinence, the rhythm method, and the
             withdrawal method are not acceptable methods of birth control. Female patients should
             also refrain from breastfeeding throughout this period.

         15. Non-sterilized males who are sexually active with a female partner of childbearing
             potential must use a male condom plus spermicide from screening through 180 days after
             receipt of the final dose of durvalumab + tremelimumab combination therapy or 90 days
             after receipt of the final dose of durvalumab monotherapy. Not engaging in sexual
             activity is an acceptable practice; however, occasional abstinence, the rhythm method,
             and the withdrawal method are not acceptable methods of contraception. Male patients
             should refrain from sperm donation throughout this period

         16. 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

         17. Body weight >30 kg

         18. Cohort specific eligibility requirements:

         19. Ability to undergo a fresh tumor biopsy for the purpose of screening for this clinical
             trial (including able and willing to give valid written consent) or the ability to
             access an available archival tumor sample taken less than 6 months prior to study
             enrollment if a fresh tumor biopsy is not feasible with an acceptable clinical risk
             and no antecedent treatment has been done.

         20. MSS tumor as documented by either: IHC testing that does not suggest loss of MLH-1,
             MSH-2, PMS2 or MSH6. OR PCR testing that does not suggest MSI

        Exclusion Criteria:

          1. Receipt of the last dose of anticancer therapy (chemotherapy, immunotherapeutic agent,
             endocrine therapy, targeted therapy, biologic therapy, tumor embolization, monoclonal
             antibodies) 30 days prior to the first dose of study drug

          2. 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 or tremelimumab may be included only after consultation
                  with the Study Physician

          3. Major surgical procedure (as defined by the Investigator) within 28 days prior to the
             first dose of the IP (investigational product, in this study, specifically durvalumab
             + tremelimumab combination). Note: Local surgery of isolated lesions for palliative
             intent is acceptable

          4. History of allogenic organ transplantation

          5. 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

          6. 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

          7. History of another primary malignancy except for

               1. Malignancy treated with curative intent and with no known active disease ≥5 years
                  before the first dose of the IP ( durvalumab + tremelimumab combination ) and of
                  low potential risk for recurrence

               2. Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease

               3. Adequately treated carcinoma in situ without evidence of disease

          8. History of leptomeningeal carcinomatosis

          9. Patients with untreated brain metastases, spinal cord compression, or leptomeningeal
             carcinomatosis should be excluded from this clinical trial because of their poor
             prognosis, because of symptoms that may arise form inflammatory reactions, and because
             they often develop progressive neurologic dysfunction that would confound the
             evaluation of neurologic and other adverse events. Patients whose brain metastases
             have been treated may participate provided they show radiographic stability (defined
             as 2 brain images, both of which are obtained after treatment to the brain metastases.
             These imaging scans should both be obtained at least four weeks apart and show no
             evidence of intracranial progression). In addition, any neurologic symptoms that
             developed either as a result of the brain metastases or their treatment must have
             resolved or be stable either, without the use of steroids, or are stable on a steroid
             dose of <10mg/day of prednisone or its equivalent and anti-convulsants for at least 14
             days prior to the start of treatment

         10. History of active primary immunodeficiency

         11. Active infection 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, or human immunodeficiency virus (positive HIV 1/2 antibodies). 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

         12. Current or prior use of immunosuppressive medication within 14 days before the first
             dose of durvalumab or tremelimumab. 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

         13. Steroids as premedication for hypersensitivity reactions (e.g., CT scan premedication)
             Receipt of live attenuated vaccine within 30 days prior to the first dose of IP. Note:
             Patients, if enrolled, should not receive live vaccine whilst receiving IP and up to
             30 days after the last dose of IP

         14. Female patients who are pregnant or breastfeeding or male or female patients of
             reproductive potential who are not willing to employ effective birth control from
             screening to 90 days after the last dose of durvalumab monotherapy or180 days after
             the last dose of durvalumab + tremelimumab combination therapy

         15. Known allergy or hypersensitivity to any of the study drugs or any of the study drug
             excipients.

         16. Prior exposure to immune mediated therapy with anti-PD-1/ anti-PDL1including
             durvalumab therapy combined with an CTLA-4 therapy including tremelimumab