Prior treatment with any PARP inhibitor Prior treatment with a PARP inhibitor Prior treatment with a known PARP inhibitor Prior treatment with a PARP inhibitor Prior treatment with any PARP inhibitor, mitoxantrone, cyclophosphamide or any platinum-based chemotherapy Patients must not have received previous treatment with PARP inhibitors Prior PARP inhibitor-based therapy Patients who have received prior inhibitor of VEGF signaling and a poly (ADP-ribose) polymerases (PARP) inhibitor administered in combination; unless administered in combination, patients who received a prior PARP inhibitor or a prior VEGF-signaling inhibitor agent are allowed after discussing with the PI Patients may not have previously received a PARP inhibitor Prior treatment with a PARP inhibitor Patients who have received prior therapy with an irinotecan-based or temozolomide-based regimen are eligible; patients who have received prior therapy with a PARP inhibitor other than talazoparib are eligible; however, patients who have progressed on a PARP inhibitor plus irinotecan regimen are not eligible Prior treatment with a PARP inhibitor in any disease setting Have demonstrated progressive disease while taking a PARP inhibitor as a previous therapy. Response to prior PARPi is not required. Prior PARP therapy could have been administered as either treatment for recurrent disease or as maintenance following prior treatment. Prior treatment with a PARP inhibitor TREATMENT: Patients who have had prior treatment with any PARP inhibitor in combination with temozolomide are ineligible to receive treatment with veliparib on this study; patients who have received prior temozolomide or PARP inhibitor with or without other chemotherapy/targeted agent aside from temozolomide should not be excluded solely because of receiving prior PARP inhibitor or temozolomide, unless it was in combination; patients who have received temozolomide with a PARP inhibitor in the past are eligible to participate but will not receive veliparib with temozolomide on study; such patients are eligible to receive other treatment regimens on study based on identified genetic mutations Prior treatment with a PARP inhibitor or topotecan No previous treatment with the specific assigned study drug or any other PARP inhibitor Patients may not have previously received a PARP-inhibitor Prior use of PARP-inhibitors No line limit on prior therapies as long as the patient meets all other eligibility criteria; patients who have received prior PARP inhibitors and/or PIkinase inhibitors are allowed to participate on the dose escalation portion; prior PARP inhibitors and/or PIKinase inhibitors excludes patients from the dose expansion cohort, but TNBC patients with BRCA mutations can go on if they had previously received a PARP inhibitor TNBC participants with BRCA mutation, unless they've had prior PARP inhibitor History of grade or toxicities with previous PIkinase inhibitor or PARP inhibitor exposure with the exception of hematologic toxicities PARP inhibitor exposure:\r\n* Part A: Patients who have received prior therapy with a PARP inhibitor, with the exception of BMN , are eligible; however, patients who have progressed on a PARP inhibitor and temozolomide regimen are not eligible\r\n* Part B and Part C: Patients who have previously been exposed to a PARP inhibitor are not eligible Phase (Part A): patients who have progressed on a PARP inhibitor and temozolomide regimen are not eligible Phase (Part B and Part C): patients who have previously been exposed to a PARP inhibitor are not eligible Patient has had prior treatment with a known PARP inhibitor Prior therapy with PARP inhibitors. Prior treatment with a PARP inhibitor (not including iniparib) Prior treatment with PARP inhibitors (Patients in Cohort A) Prior enrollment into a clinical trial of a PARP inhibitor Prior treatment with any PARP inhibitor, including rucaparib. Patients who received prior iniparib are eligible. Prior treatment with a PARP inhibitor Prior treatment with any PARP inhibitor Previous treatment with PARP inhibitor. For this study, BSI- (iniparib) is not considered as PARPi Prior treatment with a PARP inhibitor Prior treatment with a PARP inhibitor Prior treatment with PARP inhibitor. Receipt of PARP inhibitor prior to RT. Prior treatment with a PARP inhibitor. Prior treatment with any PARP inhibitor. Patients must be at least weeks from the last dose of prior PARP inhibitor Prior treatment with a known PARP inhibitor Patient has received treatment previously with a PARP inhibitor. Prior exposure to ABT or other PARP inhibitors is permitted in all cohorts except the cohort evaluating BRCA-mutated PARP inhibitor naive patients, where prior PARP inhibitor treatment will not be permitted; prior exposure to cyclin-dependent kinase inhibitors other than SCH is permitted Prior or ongoing treatment with a PARP inhibitor