Inclusion Criteria:

        Participants Enrolling to the Translational Lead-in Study:

          -  For enrollment to cohort T1: participants must have metastatic or progressive LMS with
             a) treatment with at least one prior systemic therapy b) ATRX mutation by NGS

          -  For enrollment to cohorts T2 or T3: participants must have a histologically or
             cytologically confirmed advanced solid tumor for which no standard curative therapy is
             available.

          -  For enrollment to cohort T2: participants must have a truncating ATM mutation. Testing
             may be completed via the DFCI/BWH OncoPanel, MGH SNaPshot, or any other CLIA-certified
             method.

          -  For enrollment to cohort T3, participants must have one of the following (testing may
             be completed via the DFCI/BWH OncoPanel, MGH SNaPshot, or any CLIA-certified
             laboratory):

               -  Germline mutation in BRCA1 or BRCA2 that is predicted to be deleterious or
                  suspected deleterious (known or predicted to be detrimental/lead to loss of
                  function).

               -  A somatic mutation in BRCA1 or BRCA2, or another mutation within a known HR gene
                  including BARD1, BRIP1, CDK12, CHEK2, FANCA, FANCC, FANCE, FANCF, FANCM, MRE11A,
                  NBN, PALB2, RAD51B, RAD51C, or RAD51D.

               -  A MYC amplification of greater than 6-fold.

               -  FBXW7 truncating or missense mutation designated as deleterious.

               -  CCNE1 amplification of greater than 8-fold.

               -  An ARID1A mutation as determined by the DFCI/BWH OncoPanel or any other
                  CLIA-certified method.

               -  Other (unlisted) mutations within known HR genes may be considered with approval
                  from the site principal investigator.

          -  For enrollment to cohort T4: participants must have GIST with known mutation in SDHX
             genes or loss of expression of SDHX protein(s), as determined by standard pathology
             assays. Prior therapy is not required.

          -  Age ≥ 18 years

          -  ECOG performance status ≤ 2 (Karnofsky [KPS] ≥ 60%; KPS of 50 is not permitted)

          -  Participants must have tumor amenable to biopsy, and be a candidate for tumor biopsy
             according to the treating investigator. The patient must be willing to undergo a fresh
             tumor biopsy for this study.

          -  Participants must have archival tissue available for analysis. Participants without
             available archival tissue enrolling to the translational lead-in study may instead use
             tissue from the fresh pre-treatment biopsy.

        Participants Enrolling to the Phase II:

          -  For enrollment to cohort 1A: participants must have metastatic or progressive
             osteosarcoma treated with at least one prior systemic therapy.

          -  For enrollment to cohort 1B: participants must have metastatic or progressive
             leiomyosarcoma treated with at least one prior systemic therapy.

          -  For enrollment to cohorts 2 - 5: participants must have a histologically or
             cytologically confirmed advanced solid tumor for which no standard curative therapy is
             available.

          -  For enrollment to cohort 2: participants must have a truncating ATM mutation. Testing
             may be completed via the DFCI/BWH OncoPanel, MGH SNaPshot, or any other CLIA-certified
             method.

          -  For enrollment to cohort 3A: participants must have a germline mutation in BRCA1 or
             BRCA2 that is predicted to be deleterious or suspected deleterious (known or predicted
             to be detrimental/lead to loss of function). Testing may be completed via the DFCI/BWH
             OncoPanel, MGH SNaPshot, or any CLIA-certified laboratory.

          -  For enrollment to cohort 3B: participants must have a somatic mutation in BRCA1 or
             BRCA2, or another mutation within a known HR gene including BARD1, BRIP1, CDK12,
             CHEK2, FANCA, FANCC, FANCE, FANCF, FANCM, MRE11A, NBN, PALB2, RAD51B, RAD51C, or
             RAD51D. Other (unlisted) mutations within known HR genes may be considered with
             approval from the site principal investigator.

          -  For enrollment to cohort 4A: participants must have a MYC amplification of greater
             than 6-fold or an FBXW7 truncating or missense mutation designated as deleterious, as
             determined by the DFCI/BWH OncoPanel, MGH SNaPshot, or any other CLIA-certified
             method.

          -  For enrollment to cohort 4B: participants must have a CCNE1 amplification of greater
             than 8-fold as determined by the DFCI/BWH OncoPanel, MGH SNaPshot, or any other
             CLIA-certified method.

          -  For enrollment to cohort 5: participants must have an ARID1A mutation as determined by
             the DFCI/BWH OncoPanel, MGH SNaPshot, or any other CLIA-certified method.

          -  For enrollment to cohort 1A: Age > 12

          -  For enrollment to cohorts 1B - 5: Age ≥ 18

          -  ECOG performance status ≤ 2 (Karnofsky ≥ 60%; KPS of 50 is not permitted) for
             participants ≥ 16 years of age, Lansky ≥ 50% for participants < 16 years of age

          -  Participants must have archival tissue available for analysis

        All Participants:

          -  If any participant could enroll to more than one cohort based on mutational status,
             the cohort enrollment decision will be discussed with the overall principal
             investigator. For example, if a participant has both an ATM mutation and an FBXW7
             mutation and thus could enroll to either Cohort 2 or Cohort 4A, the decision of which
             cohort to enroll to will be made in conjunction with the overall principal
             investigator. The decision as to which cohort the participant should be enrolled on
             must be made prior to the initiation of study treatment.

          -  Participants must have RECIST 1.1 measurable disease.

          -  Participants must have normal organ and marrow function as defined below:

        All Participants:

          -  Absolute neutrophil count ≥ 1,500/mcL

          -  Platelets ≥ 100,000/mcL

          -  Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN) for age

        Adult Participants (Age ≥ 18 years):

          -  AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional ULN; OR

               -  5 × institutional ULN if liver metastases are present

          -  Serum or plasma creatinine ≤ 1.5 × institutional ULN, OR

          -  Creatinine clearance ≥ 60 mL/min by Cockcroft-Gault equation for participants with
             creatinine levels above 1.5 × institutional ULN

        Pediatric Participants (Age < 18 years):

          -  ALT (SGPT) ≤ 3 × institutional (ULN)

             -for the purposes of this study, the ULN for SGPT will be defined as 45 U/L.

          -  Serum or plasma creatinine Participants 13 - 15 years: males ≤ 1.5 mg/dL, females

             ≤ 1.4 mg/dL, participants 16 - 17 years: males ≤ 1.7 mg/dL, females ≤ 1.4 mg/dL; OR

          -  Creatinine clearance ≥ 60 mL/min/1.73 m2 by Schwartz formula for participants with
             creatinine levels above the limits described above

               -  The effects of M6620 on the developing human fetus are unknown. For this reason
                  and because anti-cancer agents are known to be teratogenic, women of
                  child-bearing potential and men must agree to use adequate contraception
                  (hormonal or barrier method of birth control; abstinence) prior to study entry
                  and for the duration of study participation. Should a woman become pregnant or
                  suspect she is pregnant while she or her partner is participating in this study,
                  she should inform her treating physician immediately. Men treated or enrolled on
                  this protocol must also agree to use adequate contraception prior to the study,
                  for the duration of study participation, and 6 months after completion of M6620
                  administration.

               -  Ability to understand and the willingness to sign a written informed consent
                  document (or parent or legally authorized representative, if minor).

        Exclusion Criteria:

          -  Participants who have had chemotherapy, immune therapy, other investigational therapy,
             major surgery, or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin
             C) prior to entering the study, or participants who have not recovered to ≤ Grade 1 or
             baseline from therapies administered more than 3 weeks prior (with the exceptions of
             1. Alopecia and peripheral neuropathies which may be ≤ Grade 2 at study entry and 2.
             Laboratory abnormalities that are not listed in 3.1 and that are not considered
             clinically meaningful [e.g. decreased lymphocyte count, electrolyte abnormalities]

          -  Participants who have received oral tyrosine kinase inhibitors (TKIs) within 5
             half-lives of study entry.

          -  Participants who have previously received treatment with an ATR inhibitor, including
             but not limited to M6620 (VX-970).

          -  Participants with known untreated brain metastases should be excluded from this
             clinical trial because of their poor prognosis and because they often develop
             progressive neurologic dysfunction that would confound the evaluation of neurologic
             and other adverse events. Participants with a history of brain metastases that have
             been treated, no longer require corticosteroids, and have been stable on imaging for
             at least one month following the end of treatment are permitted.

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to M6620.

          -  Uncontrolled intercurrent illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, or psychiatric illness/social situations that would limit compliance with
             study requirements.

          -  Pregnant women are excluded from this study because M6620 is an agent with the
             potential for teratogenic or abortifacient effects. Because there is an unknown but
             potential risk for adverse events in nursing infants secondary to treatment of the
             mother with M6620, breastfeeding should be discontinued if the mother is treated with
             M6620.

          -  Known HIV-positive participants are ineligible because of the increased risk of lethal
             infections when treated with potentially marrow-suppressive therapy.

          -  Patients with a history of another malignancy are excluded with the exception of 1.
             patients who remain disease-free for 3 years and 2. adequately treated cervical
             carcinoma in situ, non-melanoma skin cancer (e.g. basal cell, squamous cell
             carcinomas), low-risk thyroid cancer.