Inclusion Criteria:

          -  Subjects must have histologically confirmed malignancy that is metastatic or
             unresectable and for which standard curative measures do not exist or are no longer
             effective

          -  Subjects will be eligible for this study based on the presence of actionable
             aberrations in one or more of the following DNA damage response (DDR) genes: ARID1A,
             ATM, ATR, ATRX, BAP1, BARD1, BRCA1/2, BRIP1, CDK12, CHEK2, FANCA, FANCC, FANCD2,
             FANCE, FANCF, FANCM, MRE11A, MSH2, NBN (NBS1), PALB2, RAD51, RAD51C, RAD51D, SMARCB1,
             and VHL, or other related genes at the discretion of the principal investigator in
             consultation with the MD Anderson Cancer Center Institute or Personalized Cancer
             Therapy Precision Oncology Decision Support (PODS) group. Variant interpretation for
             actionability will be performed by PODS

          -  The collection of archival tumor tissue (within 1 year prior to study enrollment) will
             be mandatory. Tumor biopsies on cycle 1 day 15 will be mandatory, all other biopsy
             time points are not mandatory but will be strongly encouraged where feasible. These
             include at baseline and at disease progression

          -  Subjects must have received at least 1 line of systemic therapy in the
             advanced/metastatic setting. Subjects with diseases without known effective options,
             and subjects who had declined standard of care therapy prior to study introduction are
             also eligible

          -  Subjects must have measurable disease per Response Evaluation Criteria in Solid Tumors
             (RECIST) version (v) 1.1, or patients may have bone metastatic disease evaluable by
             Prostate Cancer Working Group 3 (PCWG3) for subjects with metastatic
             castration-resistant prostate cancer (CRPC), or according to tumor evaluation criteria
             best suited and accepted for the tumor type to be evaluated

          -  Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance status 0-1

          -  Subjects must have a life expectancy >= 12 weeks

          -  Absolute neutrophil count >= 1.5 x 10^9/L

          -  Platelets >= 100 x 10^9/L

          -  Hemoglobin >= 9 g/dL or =< 5.6 mmol/L

          -  Total bilirubin =< 1.5 X the institutional upper limit of normal (ULN)

          -  Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT)/
             alanine aminotransferase (ALT) serum glutamic-pyruvic transaminase (SGPT) =< 2.5 X
             institutional ULN or =< 5 X institutional ULN in the presence of liver metastases

          -  Serum creatinine =< 2 X ULN or estimated creatinine clearance >= 30 mL/min according
             to the Cockcroft-Gault formula

          -  Female patients of childbearing potential must have a negative serum or urine
             pregnancy test at screening (and again at baseline just prior to first administration
             of study drugs)

          -  Female patients of non-childbearing potential must meet at least 1 of the following
             criteria:

               -  Achieved postmenopausal status, defined as follows: cessation of regular menses
                  for at least 12 consecutive months, with no alternative pathological or
                  physiological cause, and have a serum follicle-stimulating hormone (FSH) level
                  confirming the postmenopausal state

               -  Have undergone a documented hysterectomy and/or bilateral oophorectomy

               -  Have medically confirmed ovarian failure All other female patients (including
                  female patients with tubal ligation) are considered to be of childbearing
                  potential

          -  Women of childbearing potential and fertile men must agree to use adequate
             contraception when sexually active from signing of the informed consent form for the
             full study until at least 6 months after the last study drug administration. Patients
             must agree to utilize 2 reliable and acceptable methods of contraception
             simultaneously. A man is considered fertile after puberty unless permanently sterile
             by bilateral orchiectomy. Men taking part in this study are advised not to father a
             child during and up to 6 months after treatment; prior to treatment, advice should be
             sought for conserving sperm due to the chance of irreversible infertility as a
             consequence of treatment. Female partners of childbearing potential from male study
             patients have to use adequate contraception / birth control between signing of the
             informed consent and 6 months after the last administration of the study drug if the
             male study patient is not sterilized. The investigator or a designated associate is
             requested to advise the patient how to achieve highly effective birth control. Highly
             effective (failure rate of less than 1% per year) contraception methods, when used
             consistently and correctly, include:

               -  Combined (estrogen and progestin containing: oral, intravaginal, transdermal) and
                  progestin-only (oral, injectable, implantable) hormonal contraception associated
                  with inhibition of ovulation

               -  Intra-uterine device or intrauterine hormone-releasing system

               -  Bilateral tubal occlusion or vasectomized partner (provided that partner is the
                  sole sexual partner and has received medical assessment of the surgical success)

               -  Sexual abstinence (reliability to be evaluated in relation to the duration of the
                  clinical trial and the preferred and usual lifestyle of the patient) Male
                  patients with a female partner of reproductive potential must use a condom and
                  ensure that an additional form of contraception is also used during treatment and
                  until 6 months after last study drug administration. Patients must agree to
                  utilize 2 reliable and acceptable methods of contraception simultaneously

          -  Evidence of a personally signed and dated informed consent document indicating that
             the patient has been informed of all pertinent aspects of the study

          -  Willing and able to comply with scheduled visits, treatment plan, laboratory tests,
             and other procedures

        Exclusion Criteria:

          -  Anticancer systemic therapy or radiotherapy within 4 weeks or 5 half-lives, whichever
             is shorter prior to starting the study agents. Prior palliative radiotherapy to
             metastatic lesion(s) is permitted, ,provided it has been completed 2 weeks prior to
             study enrollment, and no clinically significant toxicities are expected (e.g.,
             mucositis, esophagitis)

          -  Known symptomatic brain metastases requiring steroids. Patients with previously
             treated diagnosed brain metastases are eligible if they have completed their treatment
             and have recovered from the acute effects of radiation therapy or surgery prior to
             study enrollment, have discontinued corticosteroid treatment for these metastases for
             at least 4 weeks and are neurologically stable

          -  Current use of immunosuppressive medication at the time of study enrollment, EXCEPT
             for the following permitted steroids:

               -  Intranasal, inhaled, topical steroids, eye drops, or local steroid injection
                  (e.g., intra-articular injection)

               -  Systemic corticosteroids at physiologic doses =< 10 mg/day of prednisone or
                  equivalent

               -  Steroids as premedication for hypersensitivity reactions (e.g. computed
                  tomography (CT) scan premedication)

          -  Subjects who had major surgery within 4 weeks prior to study enrollment

          -  Known prior severe hypersensitivity to investigational products or any component in
             their formulations, including known severe hypersensitivity reactions to monoclonal
             antibodies (National Cancer Institute [NCI] Common Terminology Criteria for Adverse
             Events [CTCAE] v5 grade >= 3)

          -  Active infection requiring systemic therapy

          -  Known history of immune-mediated colitis, inflammatory bowel disease, pneumonitis, and
             pulmonary fibrosis

          -  Active or prior autoimmune disease that may deteriorate when receiving an
             immunostimulatory agent. Patients with type I diabetes, vitiligo, psoriasis, or hypo-
             or hyperthyroid disease not requiring immunosuppressive treatment are eligible

          -  Prior organ transplantation including allogenic stem cell transplantation

          -  Diagnosis of myelodysplastic syndrome (MDS)

          -  Vaccination within 4 weeks of study enrollment and while on trial is prohibited except
             for the administration of inactivated vaccines

          -  Clinically significant (i.e., active) cardiovascular disease: cerebral vascular
             accident/stroke (< 6 month prior to enrollment), myocardial infarction (< 6 months
             prior to enrollment), unstable angina, congestive heart failure (>= New York Heart
             Association Classification class II) or a serious cardiac arrhythmia requiring
             medication

          -  Other acute or chronic medical or psychiatric conditions including but not limited to
             recent (within the past year) or active suicidal ideation or behavior or laboratory
             abnormality that may increase the risk associated with study participation or
             investigational product administration or may interfere with the interpretation of
             study results, and in the judgement of the Investigator, would make the patient
             inappropriate for entry into this study

          -  Pregnant female patients, breastfeeding female patients, fertile male patients, and
             female patients of childbearing potential who are unwilling or unable to use 2 highly
             effective methods of contraception as outlined in this protocol for the duration of
             the study, and for at least 30 days after the last dose of avelumab and at least 60
             days after the last dose of M6620 or M3814, whichever is later for the individual
             patient

          -  Hepatitis B virus (HBV) or hepatitis C virus (HCV) infection at screening (positive
             HBV surface antigen or HCV ribonucleic acid (RNA) if anti-HCV antibody screening test
             is positive)

          -  Known history of testing positive for human immunodeficiency virus (HIV) or known
             acquired immune deficiency syndrome (AIDS)

          -  Known additional malignancy that is active and/or progressive requiring treatment;
             exceptions include basal cell or squamous cell skin cancer, in situ bladder cancer, or
             other cancer for which the patient has been disease-free for >= 2 years

          -  Persisting toxicity related to prior therapy (NCI CTCAE v4 grade > 1); however,
             alopecia and sensory neuropathy grade =< 2, or other grade =< 2 AEs not constituting a
             safety risk, based on the investigator's judgement, are acceptable

          -  Subjects receiving treatment with strong inhibitors or inducers of CYP3A4 that cannot
             be discontinued before start of investigational treatment and for the duration of
             study