Inclusion Criteria:

   - Patients must have histologically confirmed metastatic or unresectable malignancy that
   is refractory to standard therapy or for which no standard therapy exists and where
   irinotecan is deemed a reasonable treatment option

   - FOR PATIENTS ENROLLED IN THE EXPANSION COHORT: Patients must have known deficiencies
   in the deoxyribonucleic acid (DNA)-Damage Response (DDR), e.g. mutations in ATM,
   PALB2, BRCA1/2 or other deficiencies after discussion with the Study Chair
   (prioritized), or patients can be enrolled with the following tumor types regardless
   of known DDR deficiency: pancreatic cancer, colorectal cancer, and small cell lung
   cancer

   - Patients must have measurable disease, defined as at least one lesion that can be
   accurately measured in at least one dimension (longest diameter to be recorded for
   non-nodal lesions and short axis for nodal lesions) as >= 20 mm (>= 2 cm) with
   conventional techniques or as >= 10 mm (>= 1 cm) with spiral CT scan, magnetic
   resonance imaging (MRI), or calipers by clinical exam

   - No limit on prior lines of therapy for metastatic disease; prior adjuvant or
   neoadjuvant chemotherapy does not count as a prior line of therapy as long as
   completion of the adjuvant or neoadjuvant therapy was more than 1 year prior to
   patient enrollment

   - Age >= 18 years. Because no dosing or adverse event data are currently available on
   the use of M6620 (VX-970, berzosertib) in combination with irinotecan in patients < 18
   years of age, children are excluded from this study, but will be eligible for future
   pediatric trials

   - Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 (Karnofsky >= 70%)

   - Life expectancy of greater than 12 weeks

   - Leukocytes >= 3,000/mcL

   - Absolute neutrophil count >= 1,500/mcL

   - Platelets >= 100,000/mcL

   - Total bilirubin within normal institutional limits

   - Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
   [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
   =< 2.5 x institutional upper limit of normal (ULN); if liver involvement, =< 5 x ULN

   - Creatinine clearance >= 60 mL/min/1.73 m^2

   - Patients must have archived tumor tissue from prior tumor biopsy or surgical
   resections available for submission that is sufficient to complete molecular profiling

   - FOR PATIENTS ENROLLED IN THE EXPANSION COHORT: Willingness to undergo mandatory
   biopsies (day -13, approximately 18 to 22 hours post end of irinotecan infusion and
   day 2, approximately 18 to 22 hours post end of irinotecan infusion [= 17 to 21 hours
   post end of M6620 (VX-970, berzosertib)]); patients enrolled to this cohort should
   have tumors deemed easily accessible for biopsies with low likelihood of complication

   - The effects of M6620 (VX-970, berzosertib) on the developing human fetus are unknown;
   for this reason and because DNA-damage response (DDR) inhibitors may have teratogenic
   potential, 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 (VX-970,
   berzosertib) administration

      - For this reason and because DNA-damage response (DDR) inhibitors may have
      teratogenic potential, 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, for the duration of study participation and for 6 months
      after study completion

   - Ability to understand and willingness to sign a written informed consent document

Exclusion Criteria:

   - Patients who have had chemotherapy or other systemic therapy or radiotherapy or
   patients who have not recovered from adverse events due to prior administered agents
   as follows:

      - Chemotherapy < 4 weeks prior to entering the study

      - Radiotherapy < 4 weeks prior to entering the study

      - Nitrosoureas/mitomycin C < 6 weeks prior to entering the study

      - Targeted therapy < 2 weeks (or 5 half-lives, whichever is longer) prior to
      entering the study

      - Those who have not recovered from clinically significant adverse events due to
      prior agents administered to grade =< 1 or baseline, with exception of alopecia
      and peripheral neuropathy, unless approved by the protocol chair

      - Immunotherapy < 4 weeks prior to entering the study

   - Patients who are receiving any other investigational agents

   - Patients with unstable brain metastases should be excluded; however, patients with
   known brain metastases may participate in this clinical trial if they are clinically
   stable (without evidence of progression by imaging for at least four 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 on a stable
   or decreasing dose of steroids for at least 14 days prior to trial treatment

   - History of allergic reactions attributed to compounds of similar chemical or biologic
   composition to M6620 (VX-970, berzosertib) or irinotecan

   - M6620 (VX-970, berzosertib) is primarily metabolized by CYP3A4; irinotecan and its
   active metabolite, SN-38, are metabolized by CYP3A4 and UGT1A1, respectively;
   therefore, concomitant administration with strong inhibitors or inducers of CYP3A4
   should be avoided; valproic acid is known to inhibit the process of glucuronidation
   and may potentially enhance the toxicity of irinotecan; medications that enhance
   glucuronidation (i.e. phenytoin, phenobarbital, carbamazepine, rifampin, etc.) may
   also enhance clearance of SN-38, which may possibly decrease efficacy; therefore,
   concomitant administration of these drugs should be avoided; because the lists of
   these agents are constantly changing, it is important to regularly consult a
   frequently-updated medical reference for a list of drugs to avoid or minimize use of;
   as part of the enrollment/informed consent procedures, the patient will be counseled
   on the risk of interactions with other agents, and what to do if new medications need
   to be prescribed or if the patient is considering a new over-the-counter medicine or
   herbal product

   - Uncontrolled intercurrent illness including, but not limited to, severe active
   infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
   arrhythmia, or psychiatric illness/social situations that would limit compliance with
   study requirements; patients with chronic viral hepatitis may participate in this
   clinical trial if they are clinically stable with acceptable liver function

   - Pregnant women are excluded from this study because M6620 (VX-970, berzosertib) as a
   DNA-damage response (DDR) inhibitor may have 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 (VX-970,
   berzosertib), breastfeeding should be discontinued if the mother is treated with M6620
   (VX-970, berzosertib); these potential risks may also apply to other agents used in
   this study

   - Human immunodeficiency virus (HIV)-positive patients with well-controlled disease, as
   determined by CD4 count and viral load, who are on antiretroviral therapy that does
   not contain a strong inducer or inhibitor of CYP3A4 (e.g. regimens containing
   ritonavir, cobicistat, efavirenz or etravirine) are allowed on trial; HIV-positive
   patients on combination antiretroviral therapy with strong inducers or inhibitors of
   CYP3A4 are ineligible because of the potential for pharmacokinetic interactions with
   M6620 (VX-970, berzosertib); patients with poorly controlled HIV are not eligible due
   to the increased risk of lethal infections when treated with marrow-suppressive
   therapy