Participant must have a confirmed germline deleterious BRCA mutation; participants with a BRCA1 or BRCA2 classified as “variant, suspected deleterious” by Myriad Genetics are also eligible for the trial; participants with only a BRCA1 or BRCA2 VUS (variant of uncertain significance) are not eligible for this study; if a potential subject is considered high risk for carrying a BRCA1/BRCA2 mutation by National Comprehensive Cancer Network (NCCN) criteria but does not have insurance coverage for testing or if results from available testing options will not be ready in time for enrollment in the study Myriad Genetic Laboratories may cover the cost of the test; genetic testing does not have to be performed by Myriad Genetic Laboratories but a study-specific test request form is available for tests submitted to Myriad; this form may also be used for genetic testing which will be covered by the participant’s insurance and may lead to more expedited testing Patients must also meet at least one of the following criteria:\r\n* Triple negative: histologically confirmed primary and/or metastatic site that is estrogen receptor (ER)-negative (=< 1%), progesterone receptor (PR)-negative (=< 1%), and HER2–negative\r\n* BRCA mutation: previously confirmed deleterious breast cancer 1, early onset (BRCA1) or breast cancer 2, early onset (BRCA2) germline mutation or suspected deleterious BRCA1 or BRCA2 germline mutation if the classification being used is the 5-tier classification; documentation of germline test results are required Patients must have adequate tissue available and must agree to have specimens submitted for germline BRCA deoxyribonucleic acid (DNA) sequencing and other correlative studies\r\n* NOTE: Blood for BRCA mutation testing is to be collected and submitted after registration but before treatment Documented germline mutation in BRCA1 or breast cancer 2, early onset (BRCA2) that is predicted to be deleterious or suspected deleterious (known or predicted to be detrimental/lead to loss of function); local germline (g)BRCA testing results, if available, will be used for establishing eligibility; if local gBRCA testing results are not available, central testing will be provided for those patients who otherwise appear to be eligible Patients who do not have deleterious or suspected deleterious gBRCA1 and/or 2 mutations but only have BRCA1 and/or BRCA2 mutations that are considered to be non-detrimental (e.g., “variants of uncertain clinical significance” or “variant of unknown significance” or “variant, favor polymorphism” or “benign polymorphism” etc.) BRCA 1/2- associated metastatic breast carcinoma BRCA 1/2-associated metastatic breast carcinoma: at least one but no more than three prior chemotherapy-containing lines. Documented germline mutation or somatic mutation (or homozygous deletion) in one of the DNA repair genes listed below that is deleterious or suspected to be deleterious; the mutation must be identified through a Clinical Laboratory Improvement Act (CLIA)-approved next generation sequencing (NGS) panel\r\n* Cohort 1: Germline mutation in one of the DNA repair genes listed below OR\r\n* Cohort 2: Somatic mutation or homozygous deletion in one of the DNA repair genes listed below or a somatic mutation of BRCA1 or BRCA2 (without germline BRCA 1 /2 mutation) \r\n* DNA Repair Gene List: ATM, ATR, BARD1, BRIP1 (FANCJ), CHEK2 , FANCA, FANCC, FANCD2, FANCE, FANCF, FANCM, MRE11A, NBN, PALB2, RAD50, RAD51C, RAD51D, plus other hormone receptor (HR)-related genes at the discretion of Dr. Tung with the key study collaborators \r\n** All deep (homozygous) deletions, frameshift mutations and truncating mutations in the genes listed above are eligible as well as missense variants in these genes that have previously been reported as pathogenic or likely pathogenic Germline BRCA1 or BRCA2 mutation Have biopsiable and evaluable disease. Note: biopsy is optional for patients known to harbor a BRCA1/2 mutation In Part B, the patients recruited to one of the eight expansion arms must have advanced solid tumors of the following types: Arm 1: Patients with relapsed, platinum-sensitive high grade epithelial, non-mucinous, ovarian cancer, fallopian tube, or primary peritoneal cancer must meet the following criteria: i. Patients must have at least 2 prior platinum-containing treatments in any treatment setting. • Note: patients could have received additional therapy after the last platinum-containing regimen if the other eligibility criteria are met. ii. Patients must have platinum-sensitive recurrent disease and must not have progressed (by RECIST v1.1 criteria) within 6 months of the completion of the last platinum containing regimen. • Note: patients can receive additional non-platinum based chemotherapy for recurrence after the last platinum containing regimen if the criteria for platinum sensitivity are met. iii. Arm 1a: Patients with relapsed, platinum-sensitive high grade epithelial, non-mucinous, ovarian cancer, fallopian tube, or primary peritoneal cancer (EOC) with either known deleterious or suspected deleterious germline or somatic BRCA1/2 mutations or with DNA HRD • If HRD or BRCA1/2 mutation status is unknown or has not been previously evaluated, then the patient must undergo tissue screening using the Myriad myChoice® diagnostic test to determine eligibility. iv. Arm 1b: Patients with relapsed, platinum-sensitive high grade epithelial, non-mucinous, ovarian cancer, fallopian tube, or primary peritoneal cancer (EOC) without either known deleterious or suspected deleterious germline or somatic BRCA1/2 mutations or without DNA HRD • If HRD or BRCA1/2 mutation status is unknown or has not been previously evaluated, then the patient must undergo tissue screening using the Myriad myChoice® diagnostic test to determine eligibility. Arm 2: Patients with triple negative breast cancer must meet the following criteria: i. Patients with either known deleterious or suspected deleterious germline or somatic BRCA1/2 mutations or with DNA HRD. • If HRD or BRCA1/2 mutation status is unknown or has not been previously evaluated, then the patient must undergo tissue screening using the Myriad myChoice® diagnostic test to determine eligibility. ii. Patients with 0-1 prior platinum-containing treatment in any treatment setting. • Note: patients could have received additional therapy after the last platinum-containing regimen if the other eligibility criteria are met. iii. Patients who have received ? 3 prior lines of therapy in the advanced or metastatic setting. Arm 3: Patients with metastatic castration-resistant prostate cancer, including but not limited to mutations in HR pathways and/or defined by HRD algorithms, and must meet the following criteria: i. Patients with either known deleterious or suspected deleterious germline or somatic BRCA1/2 mutations or with DNA HRD. • If HRD or BRCA1/2 mutation status is unknown or has not been previously evaluated, then the patient must undergo tissue screening using the Myriad myChoice® diagnostic test to determine eligibility. ii. The patient may be either chemotherapy-naïve, but must have received prior abiraterone acetate and/or enzalutamide treatment, or have previously had no more than two taxane-based chemotherapy regimens including docetaxel and carbazitaxel. If docetaxel is used more than once, this will be considered as one regimen. iii. At least 2 weeks since the completion of prior flutamide, bicalutamide, and nilutimide, or enzalutamide and abiraterone treatment. iv. At least 2 weeks from any radiotherapy, with the exception of a single fraction of radiotherapy for the purposes of palliation (confined to one field). v. Documented prostate cancer progression with one of the following: Olaparib\r\n* Patients with solid tumors that harbor DNA damage repair gene mutations as exemplified below detected by next-generation sequencing (NGS) or real-time- polymerase chain reaction (RT-PCR) in assays performed at a CLIA-certified laboratory:\r\n** Examples of DNA damage repair deficiency “BRCA-ness” (somatic mutations in tumors), but not limited to, are: breast cancer 1, early onset (BRCA 1), breast cancer 2, early onset (BRCA2)/Fanconi anemia group D1 (FANCD1), partner and localizer of BRCA2 (PALB2 or FANCN), RAD51 recombinase (RAD51), RAD52 homolog, DNA repair protein (RAD52), BRCA1 interacting protein C-terminal helicase 1 gene (FANCJ), Fanconi anemia complementation group D2 (FANCD2), 26S proteasome complex subunit DSS1 (DSS1), MRE11 homolog A, double strand break repair nuclease (MRE11), RAD50 double strand break repair protein (RAD50), nibrin (NBS1), Bloom syndrome RecQ like helicase (BLM), ATM serine/threonine kinase (ATM), ATR serine/threonine kinase (ATR), checkpoint kinase 1 (CHK1), checkpoint kinase 2 (CHK2), Fanconi anemia complementation group (FANC) A,-B,-C, -E, -F, -G,-L, M, D2 Patients with known germline BRCA mutations will be excluded from the study, however testing is not required for inclusion in the study Patients must have histologically confirmed solid malignancy (excluding lymphoma) that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective, and for which: a) there is reasonable expectation of response to the combination of carboplatin/paclitaxel OR b) breast cancer (BRCA) 1/2 germline mutation is present; results from Myriad will be acceptable; if testing for BRCA 1 and 2 germline mutations is done through another organization, a report from a genetics consult with a qualified medical professional confirming that the laboratory results show a recognized germline deleterious BRCA 1 or 2 mutation or rearrangement is required; if the latter cannot be obtained, principal investigator (PI) or study chair review of the lab results and confirmation of BRCA mutation or rearrangement will be required OR c) BRCA 1/2 somatic mutation previously identified using a Clinical Laboratory Improvement Amendments (CLIA) certified assay Cohorts 1 to 3: Have platinum-resistant disease and have documented test results assessing alterations in the BRCA1 and BRCA2 genes prior to receiving study treatment. Cohort 3: Are BRCA positive and have previously received a PARP. Patients with a deleterious or suspected deleterious BRCA1 or BRCA2 mutation (germline or somatic) Have a deleterious mutation in BRCA1/2 or ATM, or molecular evidence of other homologous recombination deficiency Patients known to have a BRCA gene mutation; genetic testing is not required Patients with clear cell or low grade ovarian cancer unless the patient has a known germline or somatic breast cancer (BRCA) mutation or a mutation in another homologous recombination gene Solid tumors with one or more of the following DNA repair defects:\r\n* BRCA1, BRCA2, ATM, BARD1, BRIP1, CDK12, CHEK2, FANCA, NBN, PALB2, RAD51, RAD51B, RAD51C, RAD51D, RAD54L (validated from archival tumor tissue or germ line testing from any Clinical Laboratory Improvement Act [CLIA] approved lab); this testing should occur prior to study consent or enrollment Eligible patients with germline or somatic BRCA mutations must have disease progression after treatment with a PARP inhibitor; patients with unknown BRCA status must undergo testing prior to enrollment; however, non-mutation patients will also be eligible for study Patients PRE-identified as having either a germline deleterious mutation or tumor expression of a deleterious mutation) as determined by next-generation DNA sequencing only, in at least one gene involved in DNA damage repair through homologous recombination including but not limited to: ARID1A, ATM, ATRX, MRE11A, NBN, PTEN, RAD50/51/51B, BARD1, BLM, BRCA1, BRCA2, BRIP1, FANCA/C/D2/E/F/G/L, PALB2, WRN, CHEK2, CHEK1, BAP1, FAM175A, SLX4, MLL2 or XRCC\r\n* Patients with somatic mutations will be PRE-identified as having a homologous recombination mutation based on next-generation sequencing (NGS) done in a Clinical Laboratory Improvement Act (CLIA) certified, College of American Pathologists (CAP) tested and bioinformatics-validated testing lab PRIOR to enrollment in this current protocol; the testing may have been done at any time prior to enrollment; HOWEVER, if any patient has had NGS testing more than 3 months prior to enrollment, or if there has been intervening therapy, then a repeat NGS test must be done and the deleterious somatic mutation must be re-identified for inclusion\r\n** The determination of a deleterious mutation must be supported in the documentation included in the testing, and should include clinical, or pre-clinical literature to support the finding that a specific mutation results in impaired function of the gene, and thus impaired DNA repair through homologous recombination; variants of unknown significance will not be eligible\r\n* Patients with germline deleterious mutations may have been identified at any time point prior to inclusion in the protocol and do NOT need to have this genetic testing repeated regardless of time frame and intervening therapy Subjects must not be a known carrier of BRCA1 or BRCA2 gene mutation For enrichment stage of trial only (if necessary): Confirmation of a suspected/known deleterious mutation in a gene of interest (ATM, BARD1, BRCA1, BRCA2, BRIP1, CDK12, CHEK1, CHEK2, FANCL, PALB2, PPP2R2A, RAD51B, RAD51C, RAD51D or other DNA repair genes) via Clinical Laboratory Improvement Act (CLIA) certified testing Patients must be germline BRCA 1 or 2 negative; (Note: if BRCA status was previously determined, that result is acceptable but documentation of status must be available; subjects with unknown status will be referred to genetic counselling for BRCA testing as per standard of care) and/or patients with previously identified genetic aberrations that are associated with HRD will be eligible even in the absence of family history [e.g. somatic BRCA mutation, Fanconi Anemia gene, ATM or RAD51 mutations] Patients must have clear and documented evidence of biallelic inactivation BRCA1, BRCA2 or ATM by sequencing, for example University of Washington (UW)-Oncoplex, SU2C, or Foundation One testing and/or patients with clearly deleterious mutations of other genes involved in homologous DNA repair (e.g., partner and localizer of BRCA2 [PALB2], BRCA1-interacting protein 1 [BRIP1], etc.) by sequencing via UW-Oncoplex, SU2C, or Foundation One testing may be included at the investigator’s discretion Patients with cytologically or histologically confirmed locally advanced or metastatic pancreas adenocarcinoma with a BRCA1 or 2 or PALB2 mutation confirmed by report from Myriad Genetics (United States of America [USA]); reports from other molecular diagnostic companies can be used to confirm mutations as well; BRCA 1 or 2 or PALB2 mutation can be confirmed locally for all international sites\r\n* For Part I, non-randomized, lead-in portion, patients with a known BRCA 1 or 2 or PALB2 mutation are eligible along with patients who potentially may have a likelihood of having a BRCA mutation (e.g., personal or family history of breast, pancreas, ovary, endometrial, prostate or other likely related malignancy); for Part I, randomized portion, a known BRCA 1 or 2 or PALB2 mutation is required PHASE II STUDY COHORT 1 OVARIAN CANCER ELIGIBILITY CRITERIA (MEDI+O, MEDI+C AND MEDI+O+C): Documentation of germline breast cancer (BRCA)1 and BRCA2 mutation (gBRCAm) status will be requested; a documented deleterious germline BRCA1 and BRCA1 mutation (gBRCAm) obtained in a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory will be requested, but it is not mandated for enrollment; Myriad testing will be accepted; if testing for BRCA is done by other organizations either by multi-gene panels or individual testing, genetic consultation report from a qualified medical professional listing the mutation and confirming that the laboratory results showed a recognized gBRCAm or germline deleterious BRCA rearrangement is required; if the patient refused genetic counseling, it should be documented in the medical records; variants of uncertain significance (VUS) of BRCA1 and BRCA2 are not considered deleterious; patients with VUS or deleterious mutation in other genes without gBRCAm or patients with negative BRCA testing are still eligible PHASE II STUDY COHORT 5 TRIPLE NEGATIVE BREAST CANCER ELIGIBILITY CRITERIA (MEDI+O ONLY)\r\nDocumentation of germline BRCA1 and BRCA2 mutation (gBRCAm) status will be requested for eligibility; a documented deleterious gBRCAm obtained in a CLIA-certified laboratory, including but not limited to Myriad Genetics, either by multi-gene panels or individual testing, will be required prior to study enrollment; variants of uncertain significance (VUS) of BRCA1 and BRCA2 are not considered deleterious mutation; patients with VUS or deleterious mutation in other genes without gBRCAm or patients with negative BRCA testing are still eligible Patients must have platinum-sensitive recurrent high-grade serous or high-grade endometrioid ovarian, primary peritoneal, or fallopian tube cancers; patients with other (clear cell, mixed epithelial, undifferentiated carcinoma, or transitional cell carcinoma) high-risk histologies are also eligible, provided that the patient has a known deleterious germline BRCA1 or BRCA2 mutation identified through testing at a clinical laboratory; Note: Due to the long acceptance of germline BRCA testing through Myriad, Myriad testing will be accepted; if testing for germline BRCA is done by other organizations, documentation from a qualified medical professional (e.g., ovarian cancer specialty physician involved in the field, high risk genetics physician, genetics counselor) listing the mutation and confirming that the laboratory results showed a recognized germline deleterious BRCA1 or BRCA2 mutation or BRCA rearrangement is required; please collect a copy of Myriad or other BRCA mutational analysis (positive or VUS or negative) reports\r\n* Platinum-sensitive disease defined as no clinical or radiographic evidence of disease recurrence for > 6 months (or 182 days) after last receipt of platinum-based therapy\r\n* Patients must have had a complete clinical response to their prior line of platinum therapy and cannot have had progression through prior platinum-based therapy No deleterious or suspected deleterious germline BRCA1 or BRCA2 mutation based on full sequencing and comprehensive rearrangement testing at an external reference laboratory; patients with variants of unknown significance will be eligible Deleterious or suspected deleterious germline or somatic gene mutation implicated in the HR pathway, excluding BRCA1 or BRCA2, based on multiplex germline gene testing or direct tumor next generation deoxyribonucleic acid (DNA) sequencing; these genes include: PTEN, PALB2, CHEK2, ATM, NBN, BARD1, BRIP1, RAD50, RAD51C, RAD51, RAD51D, MRE11, ATR, Fanconi anemia complementation group of genes (FANCA, FANCC, FANCD2, FANCE, FANCF, FANCG, FANCL), plus other HR-related genes at the discretion of the primary investigators Any patient with a deleterious mutation in BRCA1 or BRCA2 Known BRCA 1 or BRCA 2 mutation. BRCA1, BRCA2 and/or ATM gene defect. The presence of homologous recombination deficiency defined by either; A) Inherited pathogenic variant of BRCA2, ATM, BRCA1, PALB2 by a Clinical Laboratory Improvement Act (CLIA) level germline assay or B) have evidence by somatic sequencing using a CLIA level assay of biallelic inactivation of BRCA1, BRCA2, PALB2, FANCA or biallelic inactivation or monoallelic inactivating mutation of ATM. It is anticipated that the majority of patients will be germline carriers of a pathogenic variant of BRCA1, BRCA2 or ATM. Germline BRCA 1/2 Mutation Positive Documented evidence of at least ONE or MORE of the following:\r\n* Biallelic inactivation of genes involved in homologous recombination repair in the tumor\r\n* Biallelic inactivation of other genes involved in homologous DNA recombination repair in the tumor may be included at investigator’s discretion\r\n* Homologous recombination repair deficiency by genomic signature in the tumor\r\n* Clearly pathogenic or likely pathogenic germline mutation in BRCA2, BRCA1 and/or ATM\r\n* (Note: the following are not alone sufficient for eligibility and require additional criteria to be met: germline variant of uncertain significance in BRCA1, BRCA2 and/or ATM; germline mutations in other HR genes) Patients with HRD identified by one of the following criteria: a) Tested positive for BRCA 1 or 2 germline deleterious mutation, b) Previously identified genetic aberrations that are associated with HRD (e.g., somatic BRCA mutation, PALB2, Fanconi anemia gene or RAD51 mutations), c) Patients with somatic ATM loss as identifiable with immunohistochemistry or with ATM mutation, d) Pancreatic ductal adenocarcinoma (PDAC) patients with family history of 2 or more first-degree relatives with BRCA-associated cancers (stomach, breast, ovary) or 1 or more first-degree relative with PDAC Phase II only: Patients with metastatic adenocarcinoma of the pancreas with genomic markers (signature) of homologous recombination deficiency (HRD) or BRCA1 or BRCA2 or PALB2 mutation, or HRD (non-BRCA, non-PALB) who have not received any systemic therapy in the metastatic setting\r\n* NOTE: In pancreatic cancer: exposure to irinotecan is only allowed in the neoadjuvant setting and no progressive disease < 3 months from last dose of irinotecan Breast cancer in BRCA1 or BRCA2 positive ovarian cancer patients. Documented mutation of tumor protein 53 (TP53), breast cancer (BRCA)1, BRCA2, or other hereditary cancer syndromes For expansion cohort patients, the profiling must reveal at least one mutation in the following selected DNA repair genes involved in cell cycle arrest signal transduction, BRCA1 pathway, Fanconi’s proteins pathway, and RAD51 pathway: (ATR, ATM, CHEK1, CHEK2, BRCA1, BAP1, BARD1, FANCD2, FANCE, FANCC, RAD50, FANCA, RAD51, BRCA2, PALB2, CDK12 [ENSG00000167258, also known as CRK7, CRKR, CRKRS], POLE, POLD1, BRAC2, PRKDC, ERCC2, POLQ, MRE11A, NBN [MBS1]), or at least one gene amplification in FANCD2, FANCE, FANCC, FANCA, C11orf30 (EMSY)\r\n*NOTE: Tissue or blood cell free DNA are allowed for genomic profiling of tumor; profiling should have been performed at a Clinical Laboratory Improvement Act (CLIA) certified lab =< 1 year prior to registration\r\n* NOTE: Patients in the dose escalation phase are not required to have such mutations; although genomic profiling is not required for dose escalation patients, it is encouraged in these patients prior to or after study registration if feasible Patients with deleterious BRCA 1/2 mutated ovarian cancer are not eligible TREATMENT: Patients with metastatic breast cancer and BRCA mutations must have received specific PARP inhibitor therapy; if these patients have other mutations of interest as defined in the protocol, they will be eligible to receive agents based on that mutation Patients must have histologically or cytologically confirmed ovarian cancer, peritoneal cancer or fallopian tube cancer and must have a histological diagnosis of either serous or endometrioid cancer based on local histopathological findings; both endometrioid and serous histology should be high-grade for eligibility of non-mutation carriers; patients with clear cell, mixed epithelial, undifferentiated carcinoma, or transitional cell carcinoma histologies are also eligible, provided that the patient has a known deleterious germline BRCA1 or BRCA2 mutation identified through testing at a clinical laboratory\r\n* Note: Due to the long acceptance of BRCA testing through Myriad, Myriad testing will be accepted; if testing for BRCA is done by other organizations, documentation from a qualified medical professional (e.g., ovarian cancer specialty physician involved in the field, high risk genetics physician, genetics counselor) listing the mutation and confirming that the laboratory results showed a recognized germ line deleterious BRCA 1 or BRCA 2 mutation or BRCA rearrangement is required; a copy of Myriad or other BRCA mutational analysis (positive or variants of unknown significance [VUS] or negative) reports will be requested but not required for study enrollment Known BRCA1/2 status is not required for study entry; however patients known to have a germline deleterious BRCA1/2 mutation should be encouraged to consider a preoperative trial specifically designed for BRCA1/2 carriers, if available If an ovarian cancer patient has a different histology than HGSC, but has a known germline BRCA1 or BRCA2 mutation and meets all other criteria listed, that patient is eligible TNBC participants with BRCA mutation, unless they've had prior PARP inhibitor Phase I: Patients must have received at least one prior chemotherapy regimen for metastatic disease; patients with deleterious germ line mutations in breast cancer (BRCA)1 or BRCA2 are not required to have received prior chemotherapy for metastatic disease Patients must be assigned to S1400G; S1400G biomarker eligibility defined as homologous recombination repair deficiency (HRRD) positive is as follows\r\n* Biomarker-positive group\r\n** HRRD by FMI\r\n*** Homologous recombination repair deficiency by Foundation Medicine Inc., criteria\r\n* Alteration type\r\n** Truncating mutation, frameshift deletions, indels missense and nonsense mutations predicted to have functional consequence in any of the specified genes\r\n* Eligible alteration\r\n** Mutation in any one of the following critical HRR pathway genes: ATM, ATR, BARD1, BRCA1, BRCA2, BRIP1, CHEK1, CHEK2, FANCA, FANCC, FANCD2, FANCF, FANCM, NBN (NBS1), PALB2, RAD51, RAD51B (RAD51L1), RAD54L, RPA1 Suspected deleterious or deleterious BRCA1 and/or BRCA2 germline mutation. Documentation of a deleterious, suspected deleterious, or pathogenic germline BRCA1 or BRCA2 mutation from Myriad Genetics or other laboratory approved by the Sponsor Prior BRCA-associated cancer as long as there is no current evidence of the cancer Have a known BRCA 1/2 mutation status (for participants who do not have a known BRCA 1/2 status at screening, a blood sample will be collected to determine the status with the results available prior to randomization Known deleterious germline mutation of BRCA1/2 (Patients in Cohorts A and A1) Documented germline mutation in Breast Cancer susceptibility genes: BRCA1 and/or BRCA2 that is predicted to be deleterious or suspected deleterious (known or predicted to be detrimental/lead to loss of function) BRCA 1 and/or BRCA2 mutations that are considered to be non detrimental Documented Breast Cancer Gene (BRCA) germline mutation testing. Identified deleterious mutation in BRCA 1 or 2 genes (this does not include variants of uncertain significance) Deleterious or pathogenic germline BRCA 1 or BRCA 2 mutation Germline BRCA1 or BRCA2 mutation; patients with unknown BRCA status who meet NCCN BRCA screening criteria will be screened for BRCA mutation. Must have histologically or cytologically confirmed triple negative (ER-/PR-/HER2-) invasive breast cancer, stage I-III at diagnosis (AJCC 6th edition) based on initial evaluation by clinical examination and/or breast imaging. NOTE: Patients with ER+ and/or PR+ may enroll ONLY if they are known carriers of a deleterious mutation in BRCA1 or BRCA2. Patients with HER2+ tumors may not enroll regardless of BRCA status. Have a deleterious mutation in a BRCA1/2 or ATM gene No evidence of deleterious or suspected deleterious germline mutation in BRCA1 or BRCA2 genes BRCA 1/2 mutation; Note: Patients are not required to undergo BRCA1 and BRCA2 or other genetic mutation tests in order to enroll on the study. However, in the event a patient is tested and is found to be a mutation carrier, she would be excluded from the study Dose expansion cohort only: Histological or cytological confirmation of advanced unresectable solid tumors for which no standard therapy is available in patients with a known BRCA germline mutation or those with metastatic triple negative breast cancer without known BRCA mutation; for the paclitaxel cohorts, any solid tumors with potential benefit from this combination and paclitaxel Participants must have histologically or cytologically confirmed ovarian cancer, peritoneal cancer or fallopian tube cancer and must have a histological diagnosis of either high grade serous or high grade endometrioid cancer based on local histopathological findings; participants with a deleterious BRCA-mutation on a commercial Clinical Laboratory Improvement Amendments (CLIA) assay with other high-grade histologies are also eligible\r\n* Myriad testing will be accepted as documentation of a deleterious mutation; if testing for BRCA is done by other organizations, documentation from a qualified medical professional (e.g., ovarian cancer specialty physician involved in the field, high risk genetics physician, genetics counselor) listing the mutation and confirming that the laboratory results show a recognized germline deleterious BRCA1 or BRCA2 mutation or BRCA rearrangements is required to document the presence of a deleterious mutation Patients must have one of the following: somatic mutations or deletions in BRCA1 or BRCA2; genomic alterations in other BRCA pathway genes (subcohorts: a. ATM, b. PALB2, c. other genes, e.g. Fanconi Anemia genes, ARID1A, MER11, RAD50, NBS1, ATR; amplification of EMSY); or germline mutation in BRCA1 or BRCA 2 (not breast or ovarian cancer) Patients who have endometrial carcinosarcoma; patients with ovarian cancer who have histology other than high-grade serous in the absence of a deleterious BRCA mutation; if the patient has a deleterious BRCA mutation, any histology will be accepted Subjects must agree to undergo genetic counseling and breast cancer (BRCA) testing; patients in the expansion cohort must have a germline BRCA 1 or 2 mutation Germline mutation in BRCA1 or BRCA2 that is predicted to be deleterious or suspected deleterious. Metastatic breast cancer and have formalin-fixed, paraffin–embedded primary tumor available for testing BRCA1 protein expression Documented 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). BRCA 1 and/or BRCA2 mutations that are considered to be non detrimental (e.g., \Variants of uncertain clinical significance\ or \Variant of unknown significance\ or \Variant, favor polymorphism\ or \benign polymorphism\ etc.) Documented 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). BRCA1 and/or BRCA2 mutations that are considered to be non detrimental (e.g. \Variants of uncertain clinical significance\ or \Variant of unknown significance\ or \Variant, favor polymorphism\ or \benign polymorphism\ etc). Must have a documented deleterious Breast Cancer Gene BRCA1 or BRCA2 germline mutation. Have a known deleterious BRCA mutation (gBRCA or sBRCA) (as determined by a local laboratory that has received an international or country-specific, quality standards certification) Subjects who are BRCA positive. Advanced breast cancer with positive BRCA1 or BRCA2 status Recurrent, and/or metastatic germline BRCA 1/2 mutation-associated ovarian cancer, with progression on a PARP inhibitor monotherapy after attaining a response to that PARPi (CR, PR, or stable disease [SD] >= 4 months [mo]) Integral biomarkers: all patients who are eligible for the study due to a history of positive BRCA1/2 mutation must provide documented evidence of their deleterious germline mutation status, obtained in a Clinical Laboratory Improvement Amendments [CLIA]-certified laboratory, including but not limited to Myriad Genetics prior to study enrollment; variants of uncertain significance (VUS) of BRCA1/2 and BRCA1/2 somatic mutations are not considered deleterious germline BRCA1/2 mutations; due to the long acceptance of BRCA 1 and BRCA 2 mutation testing through Myriad, Myriad results will be acceptable; if testing for BRCA 1 and BRCA 2 mutation is done by other organizations, a genetic consultation report from a qualified medical professional confirming that the laboratory results showed a recognized germ line deleterious BRCA 1 or BRCA 2 mutation or deleterious BRCA 1 rearrangement is required Cancer in a patient with a known inherited susceptibility mutation in breast cancer (BRCA)1 or BRCA2 Part 1 and 2: Histologically or cytologically confirmed malignancy that is metastatic or unresectable and for which standard curative measures or other therapy that may provide clinical benefit do not exist or are no longer effective. Subjects must also 1) have a documented BRCA1 or BRCA2 mutation that is considered to be deleterious by the investigator, OR 2) have high grade serous ovarian, fallopian tube, or peritoneal cancer. Subjects with molecular features indicative of DNA repair defects (such as mutation in the Fanconi anemia pathway genes or methylation of the BRCA1 promoter) may be considered eligible for following discussion with the medical monitor. Part 3: Histologically or cytologically confirmed breast, ovarian, fallopian tube or primary peritoneal cancer that is metastatic or unresectable and for which standard curative measures or other therapy that may provide clinical benefit do not exist or are no longer effective. Platinum-resistant ovarian cancer is not permitted. Subjects must also 1) have a documented BRCA1 or BRCA2 mutation that is considered to be deleterious by the investigator and 2) have received 3 or fewer regimens of cytotoxic chemotherapy in the metastatic setting and 3) have evaluable disease as defined by RECIST 1.1 or GCIC-CA-125 criteria. A first-, second-, or third-degree relative (e.g., son, brother, nephew, or cousin) of an individual with a documented BRCA1 or BRCA2 pathogenic variant Family history suggestive of a hereditary cancer syndrome not attributable to the BRCA1 or BRCA2 mutation in their family, based on pedigree review by the study team An uncertain risk of carrying the familial BRCA1 or BRCA2 mutation (e.g., because it is not clear on what side of the family the mutation is segregating), based on pedigree review by the study team Have one or more children who are BRCA1 or BRCA2 positive Additionally, patients that have a high risk of breast cancer and are pursuing prophylactic mastectomies (for example BRCA mutation carriers) will also be considered Women who are known to be positive for the breast cancer (BRCA) mutation Have a known cancer gene mutation (such as breast cancer 1/2, early onset [BRCA 1/2]) Decided to have blood drawn for breast cancer, early onset gene (BRCA) 1/2 syndrome testing Have one blood relative with a mutation in BRCA1, BRCA2, BRIP1, PALB2, RAD51C, RAD51D, BARD1, MSH2, MSH6, MLH1, or PMS2 Have a personal or family history of any hereditary/genetic cancer syndrome such as BRCA1 and BRCA2 polymorphisms, hereditary nonpolyposis colon cancer, or familial adenomatous polyposis Known to be at high risk for breast cancer due to known or suspected pathologic BRCA mutation (i.e. first-degree relative with known mutation) or prior chest radiation therapy before age 30 BRCA 1 or 2 mutation Have a known high penetrance mutation associated with hereditary breast or ovarian cancer (including BRCA1, BRCA2, p53, PTRN, ATM, PALB2, mutations associated with the Lynch Syndrome, etc.) PILOT II: BRCA positive OR Lynch syndrome positive individuals A known deleterious mutation in BRCA1, BRCA2, PTEN, or TP53. (Note: The participant must be a documented carrier to meet this criterion. If there is a known mutation in a hereditary breast cancer susceptibility gene in a participant's family member, the participant herself must have undergone genetic testing as per National Comprehensive Cancer Network guidelines to be eligible per this criterion.) Modified Gail/CARE model risk at 5 years ? 1.67%. (Note: Risk models are to be used only if there is no known previous diagnosis of resected ductal carcinoma in situ [DCIS] or LCIS and there is no known deleterious mutation in BRCA1, BRCA2, PTEN, or TP53) 10% or more probability of BRCA mutation by BRCAPRO or similar model Documented germline pathogenic or likely pathogenic variant in the BRCA1 or BRCA2 genes Known carrier of a BRCA1 or 2 mutation Women seeking an RRSO or RRS at MSK, including breast cancer 1 (BRCA 1)/breast cancer 2 (BRCA2) mutation carriers and women with a strong family history of breast and or/ovarian cancer Subject has BRCA 1 or 2 mutations. Note: Testing will only be required for Subjects presenting with bilateral breast cancer; testing is not required for unilateral cancers Patients with known breast cancer (BRCA) mutations; patients who are not tested or whose testing result is not returned at the time of registration are not excluded from registering to this study Patients enrolling in the BRCA-deficient cohorts must have a documented BRCA1 or BRCA2 germline mutation; alternatively, patients with tumors harboring somatic BRCA mutations may also enroll after discussion with the principal investigator Premenopausal women with a documented BRCA1 or BRCA2 mutation; menopause is defined as >= 12 months of amenorrhea Women without a documented BRCA mutation No patients with known deleterious mutations in breast cancer (BRCA) genes Participants with a known BRCA 1 or 2 mutation Participants with a known breast cancer (BRCA) 1 or 2 mutation Negative for BRCA1 and BRCA2 mutations Patients must not have known deleterious mutations in breast cancer (BRCA) genes INCLUSION:\n\n All Patients\n\n 1. Male or female aged ?18 years.\n\n 2. ECOG PS score of 0-1.\n\n 3. Adequate organ function.\n\n 4. Ability to understand and willingness to sign informed consent form prior to\n initiation of study procedures.\n\n 5. Measurable disease per RECIST, OR for patients with a primary diagnosis of castration\n resistant prostate cancer, progressive disease (PD) by prostate surface antigen (PSA)\n or imaging in the setting of medical or surgical castration.\n\n 6. Documented BRCA mutation, with the following exceptions: a) Patient is intended to be\n enrolled in a Single-patient Cohort; b) Patient has an advanced DNA repair\n mutation-positive solid tumor and is intended to be enrolled in Expansion Cohort 5.\n\n Patients in the Dose-escalation Phase:\n\n 7. Locally advanced solid tumor other than a primary central nervous system (CNS) tumor\n for which the patient has received ?3 prior lines\n\n 8. Confirmed solid tumor in one of the following categories:\n\n - BRCA mutation-positive pancreatic cancer for which the patient received up to 1\n prior line of cytotoxic chemotherapy in the advanced disease setting.\n\n - Advanced BRCA mutation-positive castration-resistant prostate cancer (CRPC) for\n which the patient received up to 2 prior lines of cytotoxic chemotherapy in the\n advanced disease setting.\n\n - Advanced BRCA mutation-positive ovarian cancer for which the patient received up\n to 3 prior lines of cytotoxic chemotherapy in the advanced disease setting.\n\n - Advanced BRCA mutation-positive triple-negative breast cancer (TNBC) for which\n the patient received up to 3 prior lines of cytotoxic chemotherapy in the\n advanced disease setting.\n\n - Advanced DNA repair mutation-positive solid tumors, including, but not limited to\n BRCA and non-BRCA DNA mutations, who have received up to 3 prior lines of\n cytotoxic chemotherapy in the advanced disease setting. DNA-repair mutations may\n include, but are not limited to ATM, CHEK2, PALB2, and RAD51D. Abnormal\n homologous repair deficiency (HRD) tests will also be allowed.\n\n Note that in both dose escalation and dose expansion portions of the study, prior targeted\n therapy including prior poly ADP ribose polymerase (PARP) inhibitor therapy, prior\n immunotherapy, or prior hormonal therapy is permissible. Patients with castration resistant\n prostate cancer may have received unlimited prior hormonal therapies.\n\n EXCLUSION:\n\n 1. History of leptomeningeal disease or spinal cord compression.\n\n 2. Underwent major surgery within 4 weeks before first treatment.\n\n 3. Received cancer-directed therapy 14 days (6 weeks for mitomycin C and nitrosoureas)\n before start of treatment.\n\n 4. Grade 2 or greater peripheral neuropathy at start of treatment.\n\n 5. If female, pregnant or breast-feeding.\n\n 6. Known human immunodeficiency virus (HIV) infection or hepatitis B or C infection\n\n 7. Any primary brain tumor (e.g., astrocytoma, glioblastoma).\n\n 8. Hypersensitivity or history of anaphylactic reaction to any platinum-containing\n agents. Patients must have BRAF V600E or BRAF V600K mutation identified by a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory; acceptable analytic techniques include but are not restricted to deoxyribonucleic acid (DNA) sequencing, pyrosequencing, polymerase chain reaction (PCR), melting point assays, and immunohistochemistry Patients must have BRAF V600 mutation, identified by a Food and Drug Administration (FDA)-approved test at a Clinical Laboratory Improvement Act (CLIA)-certified lab; if test at CLIA-certified lab used a non-FDA approved method, information about the assay must be provided (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) Histologically proven papillary craniopharyngioma as documented by central pathology review with positive BRAF V600E mutation by IHC Group 2: Melanoma: All patients must have been tested for BRAF mutations. Patients with V600 mutation positive melanoma must have clinical or radiological evidence of disease progression during or after treatment with a BRAF inhibitor alone or in combination with other agents. Patients must have histologically confirmed diagnosis of stage IV metastatic melanoma positive for BRAF V600E by a Clinical Laboratory Improvement Amendments (CLIA) approved assay If BRAF mutation status is unknown, before randomization the subject must have BRAF testing performed using an approved assay method. No known activating mutations in KRAS, NRAS, HRAS and BRAF Patients with melanoma should have unresectable or metastatic disease; melanoma patients with BRAF V600E or V600K mutation-positive melanoma who have previously received a BRAF inhibitor with or without a MEK inhibitor) are eligible Tumors harboring known activating KRAS, NRAS, HRAS, BRAF or PTPN11 (SHP2) mutations. Malignancy of non-squamous histology that carries a BRAF, KRAS, NRAS or HRAS mutation(s). BRAF mutation in loci other than V600 (BRAF nonV600 MUT) or BRAF fusion detected by genetic testing of the primary tumor or regional/distant metastasis BRAF mutation-positive (V600 E or K) melanoma for Parts 1, 2 and 3, or for Parts 1, 2, 4 and 5 only BRAF mutation-negative (wild type) melanoma with documented progression of >=1 measurable lesion after prior therapy (if prior therapy was received). The inclusion criterion does not apply to participants with solid tumors in Parts 4 and 5 (dose confirmation only). Prior systemic therapy (for participants who are BRAF mutation-positive), or BRAF mutation-negative and has received >1 prior systemic therapy for metastatic melanoma BRAF mutation-positive and has received prior systemic therapy with ipilimumab or other anti-cytotoxic T-lymphocyte antigen 4 (CTLA-4) blocking antibodies. The BRAF exclusion criterion does not apply to participants with solid tumor in Parts 4 and 5 (dose confirmation only). Patients must have histologically confirmed, BRAF-mutant (V600E/K) melanoma (molecularly confirmed using validated, commercially available assay performed in a Clinical Laboratory Improvement Act [CLIA]-approved laboratory) that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective\r\n* If test at CLIA-certified lab used a non-Food and Drug Administration (FDA) approved method, information about the assay must be provided; (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) BRAF V600 mutation-positive malignancy For enrollment to the phase I portion: participants must have a histologically confirmed melanoma with a BRAF V600E or BRAF V600K mutation (identified via Next Generation [NextGen] sequencing using the Dana Farber Cancer Institute [DFCI]/Brigham and Women's Hospital [BWH] OncoPanel or any Clinical Laboratory Improvement Act [CLIA]-certified method) that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective For enrollment to the phase II portion: participants must have a histologically confirmed melanoma with a BRAF V600E or BRAF V600K mutation (identified via NextGen sequencing using the DFCI/BWH OncoPanel or any CLIA-certified method) and have had progression of disease on prior BRAF and MEK inhibitor therapy Has testing for a BRAF mutation prior to study entry Have documentation of V600-activating BRAF mutation status or consent to BRAF V600 mutation testing during the screening period. Patients whose melanomas harbor a BRAF V600E or V600K mutation must have progressed on a RAF inhibitor; patients who had to discontinue RAF inhibitor therapy because of toxicity but who did not progress will be eligible unless they responded to therapy; in that case, they will not be eligible unless they progress For enrollment to the phase I portion: participants must have a histologically confirmed melanoma with a BRAF V600E or BRAF V600K mutation (identified via next generation [NextGen] sequencing using the Dana-Farber Cancer Institute [DFCI]/Brigham and Women's Hospital [BWH] OncoPanel or any Clinical Laboratory Improvement Act [CLIA]-certified method) that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective For enrollment to the phase II portion: participants must have a histologically confirmed melanoma with a BRAF V600E or BRAF V600K mutation (identified via NextGen sequencing using the DFCI/BWH OncoPanel or any CLIA-certified method) and cannot have received prior BRAF or MEK inhibitor therapy Negative result of BRAFV600E and BRAF Ins T screening test Only patients with v-raf murine sarcoma viral oncogene homolog B (BRAF) V600E or V600K mutated tumors will be enrolled Patients whose BRAF V600E mutation status is unknown, have the BRAF V600E mutation and are responding to a BRAF inhibitor or MEK inhibitor therapy, or have the BRAF V600E mutation and have not been offered the option of receiving a BRAF inhibitor or MEK inhibitor therapy for the treatment of their melanoma Participant is willing to sign a screening consent and provide pre-trial tumor material for BRAF testing (both for BRAF V^600E mutation and BRAF KIAA1549 fusion assessments)\r\n* All patients who are candidates for enrollment in stratum 5 based on their tumor histology must be pre-screened\r\n* Screening may be applied to potential stratum 1 and 2 patients Patients whose prior BRAF testing was performed at another lab (Clinical Laboratory Improvement Amendments [CLIA]/College of American Pathologist [CAP] certified or otherwise) must send additional tumor material to Brigham and Women's Hospital (BWH) for confirmation; however, to preserve available tumor material, patients whose tumor material has previously undergone BRAF analysis at the Lindeman and Ligon Labs at Brigham and Women’s Hospital using the same procedures as described in this protocol, will not be required to submit additional tumor material for analysis; these patients must have both the BRAFV600E mutation and BRAF KIAA1549 fusion assessments done and if only one test was previously conducted; additional tissue will be required for the second test For Dose-Escalation Phase: Patients must have histologically confirmed, BRAF-mutant (V600E/K) malignancy molecularly confirmed using Cobas assay or a comparable Food and Drug Administration (FDA)-approved assay (for exceptions, see below*) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy or not previously received BRAF targeted therapy, and for which standard curative or palliative measures do not exist or are no longer effective.\r\n* If test at Clinical Laboratory Improvement Act (CLIA)-certified lab used a non-FDA approved method, information about the assay must be provided to the overall principal investigator (PI) for approval. (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF detection kit and Cobas 4800 BRAF V600 mutation test). For Dose-Expansion Phase: Patients must have histologically confirmed, BRAF-mutant (V600E/K) melanoma (molecularly confirmed using Cobas assay or a comparable FDA-approved assay (for exceptions, see below*) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy at full dose or not previously received BRAF targeted therapy.\r\n* If test at CLIA-certified lab used a non-FDA approved method, information about the assay must be provided to the overall principal investigator (PI) for approval. (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF detection kit and Cobas 4800 BRAF V600 mutation test). Participants must have BRAFV600-mutation status known (molecularly confirmed using validated, commercially available assay performed in a Clinical Laboratory Improvement Act [CLIA] approved laboratory)\r\n* If test at CLIA-certified lab used a non-Food and Drug Administration (FDA) approved method, information about the assay must be provided; (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) Harboring a mutation in the BRAF oncogene or the KRAS or the NRAS oncogene Presence of KRAS or BRAF mutation in tumor tissue Histologically confirmed metastatic melanoma (stage IV) or unresectable stage III; patients with BRAF or BRAF-wild-type are eligible; only BRAF V600 mutated melanoma will be eligible for the triplet arm while BRAF-wild-type or NRAS-mutated melanoma will be eligible for the doublet arm Known or ordered molecular testing for MSI, BRAF, and KRAS status One of the following:\r\n* Documentation of BRAF V600E mutation and inability to access BRAF inhibitor or prior treatment with a BRAF inhibitor discontinued due to intolerable side effects or toxicity prior to progression OR\r\n* Documentation of wild-type BRAF V600 mutational status Participants with age greater than or equal to (>=) 18 years with either unresectable Stage IIIC or Stage IV metastatic melanoma positive for the BRAF V600 mutation, or other malignant tumor types that harbor a V600-activating mutation of BRAF CAPMATINIB INCLUSION CRITERIA: Documentation of absence of activating and targetable BRAF or NRAS point mutations REGORAFENIB INCLUSION CRITERIA: Documentation of absence of activating and targetable BRAF or NRAS point mutations ENTRECTINIB INCLUSION CRITERIA: Documentation of absence of activating and targetable BRAF or NRAS point mutations Patients must have a histologically or cytologically confirmed solid malignancy that is metastatic or unresectable for which standard curative or palliative treatments do not exist or are no longer effective\r\n* Hepatocellular carcinoma (HCC) patients are not required to have histologically or cytologically confirmed malignancy, patients are considered eligible based on tumor markers and/or imaging assessment\r\n* Patients with the following tumor types will be excluded from the normal and mild cohorts:\r\n** Pancreatic cancer patients\r\n** Colorectal cancer patients \r\n** BRAF V600E melanoma patients who have failed BRAF inhibitors\r\n*** Note: Patients with pancreatic cancer, colorectal cancer, and BRAF V600E melanoma patients who have failed BRAF inhibitors are allowed to enroll in the moderate and severe cohorts provided the patients: 1) sign a separate consent form which outlines the extremely limited activity observed in prior studies, and 2) are consented to the study by a protocol-specified designee who is not their longitudinal oncologist Histologically and/or cytologically confirmed, non-small cell lung cancer (NSCLC) of adenocarcinoma histology at the time of initial diagnosis.\r\na) Mixed tumors will be categorized by the predominant cell type; (Note: If small cell elements are present the patient is ineligible)\r\nb) Known mutational status of KRAS and BRAF oncogenes.\r\nc) For patients in whom mutational testing result is unknown or unavailable from a prior test, KRAS and BRAF testing will be performed (at a CLIA-certified laboratory) using an archived or fresh biopsy as per Standard of Care, prior to enrollment. B-Raf proto-oncogene, serine/threonine kinase (BRAF) V600E or other known dabrafenib sensitive BRAF mutation in tumor by any Clinical Laboratory Improvement Amendments (CLIA) certified lab; may include, for example, Sanger sequencing, SNaPshot platform, immunohistochemistry, Foundation One tests, etc.) COHORT B: Confirmation in a CLIA certified laboratory that one of the patient’s thyroid tumors (primary tumor, recurrent tumor, or metastasis) does not have any of the following mutations:\r\n* Mutation at V600 of the v-raf murine sarcoma viral oncogene homolog B (BRAF) gene\r\n* Mutation in NRAS or KRAS or HRAS at G12, G13, or Q61\r\n* These patients will be designated “BRAF/RAS wild type (WT)” Patients must have histologically confirmed, BRAF-mutant (V600E/K) solid tumor (molecularly confirmed using Cobas assay or a comparable Food and Drug Administration [FDA]-approved assay) that is metastatic or unresectable, have received and tolerated prior BRAF or BRAF and MEK inhibitor (BRAF targeted) therapy at full dose or not previously received BRAF targeted therapy, and for which standard curative measures do not exist or are no longer effective\r\n* If test at Clinical Laboratory Improvement Act (CLIA)-certified laboratory (lab) used a non-FDA approved method, information about the assay must be provided; (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) Any patient with metastatic melanoma from any site whose tumor is BRAF V600E mutation (V600EBRAF) positive, regardless of prior treatment will be eligible; these include untreated patients or those treated with chemotherapy, biochemotherapy or a prior BRAF-inhibitor Patients must have undergone/undergo testing for v-raf murine sarcoma viral oncogene homolog B1 (BRAF) V600 mutation status Stage IV patients must have refused, be ineligible for, or have failed at least one non-vaccine based systemic therapy (such as, high dose IL-2, dacarbazine/temozolomide, ipilimumab, or participation in a clinical trial); patients who are BRAF V600E mutation positive need to have failed, refused, or be ineligible for at least 2 lines of therapy (vemurafenib plus one other regimen) Group 1: BRAF mutant melanoma (Part B) Patients whose tumors harbor the BRAF V600E mutation, must have demonstrated progression on or intolerance to the combination of dabrafenib and trametinib Sufficient tumor available to determine if expresses wild-type or mutated BRAF if result not already known; the presence or absence of BRAF mutation needs to be determined at Brigham and Women's Cancer Center (BWH), or by Drs. Christopher Corless and Michael Heinrich at Cancer Pathology Shared Resource Oregon Health & Science University, or in context of eligibility assessment after signing consent to a previous clinical trial Agreement to allow tumor to be evaluated for mutations in KIT and BRAF BRAF- or MEK-mutation melanoma tumor status will be established prior to entry based on previous BRAF-gene analysis or MEK pathway mutation reports from a CLIA qualified laboratory. If a report is not available, the mutation analysis will be performed at Screening on archival tissue Documented wild-type in KRAS and NRAS (codons 12, 13, 59, 61, 117, and 146) and in BRAF codon 600, based on tumor tissue taken from primary or metastatic site and tested for biomarkers Confirmed wild-type status in KRAS exons 2, 3, and 4; NRAS exons 2, 3, and 4; and BRAF, by standard of care testing of tumor specimen; tissue used for testing may have been collected prior to treatment with cetuximab Patient must have been already tested and have available results of the mutations status of KRAS/NRAS/BRAF and EGFR from the circulating tumor DNA within 10 weeks prior to starting study therapy In cohort 3, must not have EGFR ectodomain mutation or any mutations in KRAS, NRAS, or BRAF Unresectable or metastatic melanoma with known v-raf murine sarcoma viral oncogene homolog B (BRAF) mutation status Patients must have known v-raf murine sarcoma viral oncogene homolog B1 (BRAF) mutational status of tumor; wild-type (WT) or mutated, prior to randomization TREATMENT: Patients with melanoma and known v-raf murine sarcoma viral oncogene homolog B (BRAF) V600E mutations must have received and progressed on specific BRAF inhibitor therapy Patients must have BRAFV600E or BRAFV600K mutations, identified by a Food and Drug Administration (FDA)-approved test at a Clinical Laboratory Improvement Amendments (CLIA)-certified lab; if test at CLIA-certified lab used a non-FDA approved method, information about the assay must be provided; (FDA approved tests for BRAF V600 mutations in melanoma include: THxID BRAF Detection Kit and Cobas 4800 BRAF V600 Mutation Test) Patients with wild type BRAF gene molecular results on ECD affected tissue Patients must have measurable and histologically or cytologically confirmed thyroid cancer with a BRAF V600E or V600K (c. 1799 T to A and c.1799_1800TG>AA) mutation that is not considered curable by surgery; confirmation will be done at Memorial Sloan Kettering (MSK); only tumors with a BRAFV600E or BRAFV600K mutation will be eligible for the clinical study; BRAF status will be assessed in a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory; BRAF status may also be tested with any Food and Drug Administration (FDA)-approved test (such as Cobas 4800 BRAF V600 Mutation Test) Tumor may have a v-raf murine sarcoma viral oncogene homolog B (B-RAF) V600 mutation or be BRAF wild type, and patients must not have been previously treated with ipilimumab Patients may have been previously treated for metastatic disease, or may have not had prior systemic treatment; patients with a V600 BRAF mutated tumor may have previously received a prior BRAF inhibitor Tumor must have a v-raf murine sarcoma viral oncogene homolog B (B-RAF) V600E, D or K mutation by Cobas pyrosequencing assay or equivalent Documentation of V600E-activating BRAF mutation status. Melanoma\r\n* Unresectable or metastatic disease progression following a B-Raf proto-oncogene, serine/threonine kinase (BRAF) inhibitor if BRAF V600 positive\r\n* Note: prior therapy with ipilimumab not required Patients BRAF mutation status must be known Inability to assess BRAF or NRAS mutation status; hypersensitivity to digoxin Patients must have their tumor sent for v-Raf murine sarcoma viral oncogene homolog B1(BRAF) mutational analysis Either treatment naïve or received only one line of systemic anticancer therapy if v-raf murine sarcoma viral oncogene homolog B1 (BRAF) wild-type or up to two lines of systemic anticancer therapy including one BRAF inhibitor-containing regimen if BRAF mutant. Treatments given in an adjuvant setting (eg, interferon, radiotherapy, isolated limb perfusion, or investigational agents) are not considered as prior lines of therapy. No prior talimogene laherparepvec, other oncolytic virus therapies, or tumor vaccines are allowed, even if given in the adjuvant setting. BRAF V600 mutation status of the current primary tumor or involved lymph node determined to be positive using the cobas BRAF V600 mutation test Those with BRAF wild type may have had a maximum of two previous systemic regimens for the treatment of melanoma. Those with a BRAF mutation may have had a maximum of three previous systemic regimens for the treatment of melanoma. For patients with metastatic melanoma not of uveal origin, v-raf murine sarcoma viral oncogene homolog B1 (BRAF) V600 mutation determination using a Clinical Laboratory Improvement Amendments (CLIA)-approved testing method on metastatic tumor tissue\r\n* NOTE: patients with metastatic melanoma of uveal origin do not need to have formal BRAF testing due to low probability of a BRAF V600 mutation in their metastatic tumor Patients must have received a biologic therapy (interleukin 2 or ipilimumab) and a BRAF and/or MEK inhibitor (if tumor contains the V600E or V600K mutation) for metastatic disease; if patient did not receive such agents, rationale for not treating the patients with the agent must be cleared study principal investigator (PI) (ie no V600e/k BRAF mutation or patient with autoimmunity, thus not eligible for biologic therapy) Evaluation of v-raf murine sarcoma viral oncogene homolog B (BRAF)V600 mutation status The tumor tissue must have been determined to be KRAS, NRAS, BRAF, PIK3CA wild-type by central CLIA testing. Must have a a BRAF V600E mutation-positive tumor as confirmed by an approved local laboratory or a sponsor designated central reference laboratory. All subjects must provide an archived or fresh tumor sample (for solid tumors) or a fresh BM aspirate and peripheral blood sample (for HCL and MM) for confirmation testing of the BRAF V600E mutation by a sponsor designated central reference laboratory using a sponsor designated assay Presence of BRAF V600E or V600K mutation in tumor tissue prior to randomization Willing to provide tissue as required per protocol for central BRAF^V600X mutation testing\r\n* NOTE: patients with prior BRAF^600X testing that demonstrate a mutation at V600X will be allowed to enroll prior to central testing if the assay was performed at a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory assay; this includes THxID, BRAF Detection Kit, Cobas 4800 BRAF600 mutation test and other CLIA-certified assays available at participating institutions Patients with unknown BRAF^600X status: histologically confirmed melanoma, papillary thyroid, cholangiocarcinoma or testicular cancer that is metastatic or unresectable and for which the investigator feels a BRAF^600X targeted agent is a reasonable treatment\r\n* NOTE: patient must be screened by central BRAF testing and must demonstrate a V600 mutation prior to start of study agent\r\n* Note: other tumor types without known BRAF^600X mutations will not be eligible for central testing Patients with known BRAF^V600X mutation: patients must have BRAF^V600X mutated, histologically confirmed cancer that is metastatic or unresectable and for which curative or standard therapies do not exist or are no longer effective\r\n* NOTE: colorectal cancers with BRAF mutations ARE NOT allowed\r\n* NOTE: any mutation at the V600 position that results in a change from V (valine) is allowed; this includes E, D, K, R or other mutations not noted here at the V600 position Patients must have BRAF^V600 mutant metastatic cancer irrespective of the histology or prior therapy; BRAF^V600 mutant status must be documented by a Clinical Laboratory Improvement Amendments (CLIA)-certified laboratory; use of an Food and Drug Administration (FDA)-approved test is preferred although other BRAF tests at a CLIA-certified laboratory may also be accepted Patients must have histologically confirmed diagnosis of stage IV metastatic melanoma positive for BRAF V600E mutation by either the COBAS test or other Clinical Laboratory Improvement Amendments (CLIA) approved assay Histologically confirmed V600E or V600K BRAF mutant melanoma Presence of BRAF mutation or genes fusion involving BRAF in tumor tissue Unknown BRAF status A documented BRAF V600E or BRAF V600K mutation by genotyping or immunohistochemistry (IHC) performed by a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory Confirmation of BRAF mutation-positive malignancy is required for selection of patients for vemurafenib therapy Melanoma with BRAF V600E or V600K mutation-positive melanoma must have progressed on, or were intolerant to, prior BRAF- or MEK-inhibitor therapy Positive proto-oncogene B-Raf (BRAF) mutation result (Cobas 4800 BRAF V600 Mutation Test) Confirmation in a CLIA certified laboratory or in an FDA-approved assay that one of the patient's thyroid tumors (primary tumor, recurrent tumor, or metastasis) possesses a BRAF mutation at V600. Patients with metastatic or locally advanced and unresectable BRAF wild-type melanoma who have either progressed following previous treatment of immunotherapy, or are not eligible for immunotherapy; patients are defined as \BRAF wild-type\ if they test negative for V600 mutations based on a Clinical Laboratory Improvement Amendments (CLIA) certified assay Patient has disease that tests positive for BRAF V600 mutations based on the results of a CLIA certified assay Histologically-confirmed metastatic melanoma (Stage IV), carrying BRAF V600E or V600K mutation as determined by testing certified for clinical diagnostic purposes. Previously performed certified BRAF testing is acceptable. If no prior BRAF mutation testing results are available, testing of a distant metastasis is preferred, but testing of a regional metastasis or primary tumor is also acceptable Only patients with v-raf murine sarcoma viral oncogene homolog B (BRAF) V600E mutated tumors will be enrolled B2: Recurrent or unresectable low grade gliomas with BRAF tandem duplication with fusion B4: BRAF V600 mutant tumors. Tumors that have been documented by CLIA or equivalent certified laboratory test to harbor BRAF V600 mutation at diagnosis or relapse BRAF V600 mutation-positive tumor as confirmed in a Clinical Laboratory Improvement Amendments (CLIA)-approved laboratory or equivalent (the local BRAF testing may be subject to subsequent verification by centralized testing; centralized testing can confirm V600E and V600K mutations only). Melanoma must be documented to contain a v-raf murine sarcoma viral oncogene homolog B1 (BRAF) V600 mutation by a Clinical Laboratory Improvement Amendments (CLIA) approved assay Measurable metastatic melanoma that expresses the V to E v-raf murine sarcoma viral oncogene homolog B (BRAF) mutation and V to K BRAF mutation assessed in a Clinical Laboratory Improvement Amendments (CLIA) certified laboratory Must have histologically confirmed cutaneous metastatic melanoma (Stage IV) that is BRAF mutation-positive (V600 E/K) as determined via central testing with a BRAF mutation assay. BRAF mutation positive melanoma or colorectal cancer; other BRAF mutation positive tumor types may be considered. Presence of BRAF V600E mutation in tumor tissue Patients with either unresectable Stage IIIc or Stage IV metastatic melanoma positive for the BRAFV600 mutation or other malignant tumor type that harbors a V600-activating mutation of BRAF, as determined by results of cobas® 4800 BRAF V600 mutation test or a DNA sequencing method, and who have no acceptable standard treatment options BRAF V600E mutation Patients with melanoma must also meet the following criteria: a. If melanoma is BRAF wild-type or has BRAF mutations that are not amenable to BRAF inhibitor therapy, and the patient is a candidate for immunotherapy, must have received ipilimumab; b. If melanoma is positive for the V600E or V600K BRAF mutation, must have received at least one line of prior therapy with a BRAF-specific inhibitor; either alone or in combination. BRAF V600E mutation detected in the primary tumor or the recurrent/persistent tumor