A Study of LY2606368 (Prexasertib) in Patients With Solid Tumors With Replicative Stress or Homologous Repair Deficiency

Inclusion Criteria: * Participants must have a pathologically confirmed advanced solid tumor for which standard therapy proven to provide clinical benefit does not exist or is no longer effective. * Participants must have one of the following (confirmed via targeted NextGeneration sequencing \[NGS\] using the DFCI/BWH OncoPanel or another CLIA-certified method): * For the replicative stress cohort: MYC amplification, CCNE1 amplification, Rb loss, FBXW7 mutation, or another genomic abnormality indicative of replicative stress as agreed upon with the principal investigator. OR * For the HR deficiency cohort: genomic or somatic mutation in BRCA1, BRCA2, PALB2, RAD51C, RAD51D, ATR, ATM, CHK2, the Fanconi anemia pathway genes, or another genomic or somatic mutation in a known HR gene as agreed upon with the principal investigator. * For the CCNE1 cohort: CCNE1 amplification of 6-fold or greater. Patients with borderline amplification levels may be considered following approval from the overall principal investigator. * Participants 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 with conventional techniques or as ≥ 10 mm with spiral CT scan, MRI, or calipers by clinical exam. * Age ≥ 18 years. * ECOG performance status \< 2 * Participants must have adequate organ and marrow function as defined below: *…