No more than prior systemic treatment regimens for advanced PNET Has received at least prior regimens of standard treatment Received =< four () prior chemotherapy regimens in the metastatic setting Received ? prior chemotherapy regimens and have relapsed or progressive disease as confirmed by radiologic assessment UCC and SCCHN and salivary gland cancer - No more than three different prior treatment regimens in the advanced/metastatic setting with a maximum of two chemotherapy-containing regimens Patients may have had up to prior regimens for metastatic disease Evidence of progressive disease during or following no more than prior chemotherapy regimens Receipt of more than prior regimens of cytotoxic chemotherapy for metastatic disease unless prior approval is granted by the Sponsor. Have previously received at least but no more than previous systemic regimens for the treatment of DLBCL Part B) Combination Arm: HER-positive disease and received at least prior cytotoxic regimens in the incurable, unresectable, LA/MBC setting (not enrolling new patients); Progressive disease after >= prior chemotherapy regimens Progressive disease after - prior chemotherapy regimens (perioperative chemotherapy within months will be considered one regimen) There is no limit to the number of prior chemotherapy regimens received; patients must have received at least one line of prior systemic chemotherapy for advanced unresectable and/or metastatic disease Chemotherapy refractory large cell and high grade NHL (i.e., progressive disease after > salvage regimens) Having progressed on at least one prior line of therapy, histologically or cytologically confirmed diagnosis of one of the following: \r\n* Dose escalation and expansion cohorts:\r\n** Checkpoint inhibitor naive non-small cell lung cancer patients must have progressed on front-line therapy cytotoxic chemotherapy and may have received up to two prior treatment regimens provided no regimens included an anti-PD or PD-L agent or an oral VEGF TKI. Prior bevacizumab or ramucirumab is allowed.\r\n** Progressed on checkpoint inhibitor non-small cell lung cancer patients must have progressed on front-line checkpoint inhibitor therapy and may have received up to two prior treatment regimens provided no regimens included an oral VEGF TKI. Prior bevacizumab or ramucirumab is allowed.\r\n** Thymic carcinoma patients must not be eligible for surgical resection at the time of enrollment and may have received any number of prior lines of therapy provided no regimens included an anti-PD or PD-L agent or an oral VEGF TKI. Prior bevacizumab or ramucirumab is allowed. Patients who received imatinib and or other TKIs as prior treatment regimens. Patients who experienced intolerance to prior therapies must have objective disease progression prior to enrollment onto BLU-- study. Patients who have received more than different prior TKI treatment regimens. More than two prior cytotoxic chemotherapy regimens for the treatment of mCRPC Part A patients who have received more than prior cytoreductive chemotherapy regimens. Patients must have had at least two prior chemotherapeutic or biologic (e.g. rituximab alone) regimens and not currently eligible for standard curative options; steroids alone and local radiation do not count as regimens Patients previously treated with chemotherapy must have no more than two prior chemotherapy regimens for the treatment of metastatic prostate cancer Treatment with chemotherapy within days of registration including subjects who received more than chemotherapy regimens in the metastatic setting at any time prior to registration Participants may have received - prior chemotherapeutic regimens for metastatic breast cancer and must have been off treatment with chemotherapy for at least days prior to registration; participants should also be adequately recovered from acute toxicities of prior treatment Patients must have NOT received more than two total prior lines of cytotoxic chemotherapy for management of recurrent or persistent disease, including re-treatment with initial chemotherapy regimens Up to prior chemotherapy regimens or metastatic disease Received at least prior chemotherapy-containing regimens. Received fewer than prior chemotherapy-containing regimens. Subjects have received at least two standard chemotherapy regimens for which they would be considered eligible (at least one containing a -fluoropyrimidine), or systemic chemotherapy is not indicated in the setting of low volume metastatic disease No more than prior regimens of cytotoxic chemotherapy unless approved by the sponsor (Note: all platinum-containing regimens are not to be counted separately but are considered to be a single regimen for the purposes of this criterion) Have previously received prior treatment with at least but no more than chemotherapy regimens in the metastatic setting. Received or more prior myelotoxic treatment regimens Patient must have received =< prior cytotoxic regimens in the metastatic setting Patients receiving any other investigational agents and or more that two different chemotherapy regimens for treatment of metastatic disease Patients with any prior chemotherapy regimens are eligible Candidates for reduced intensity conditioning regimens Patients may be enrolled in the study regardless of prior chemotherapy regimens No more than two prior cytotoxic chemotherapeutic regimens for metastatic breast cancer; in addition, prior trastuzumab emtansine (TDM-, Kadcyla) is allowed Received or more prior myelotoxic treatment regimens For both the extension and expansion cohorts, patients must have received or refused first line standard systemic therapy for their metastases (if applicable) and patients (pancreatic and esophageal cancers) must have received no more than two prior cytotoxic chemotherapy regimens in the last two years after standard therapy; patients (breast, ovarian and gastrointestinal cancers) must have received no more than three prior cytotoxic chemotherapy regimens in the last two years after standard therapy Chemotherapy refractory large cell and high grade NHL (i.e. progressive disease after > salvage regimens) Chemotherapy refractory large cell and high grade NHL (i.e., progressive disease after > salvage regimens) Has received - prior chemotherapy regimens including taxanes in advanced setting Additional Inclusion Criteria for Dose Expansion Part Only: Patients who have received more than systemic cytotoxic chemotherapy regimens for metastatic urothelial carcinoma\r\n* Note: prior perioperative chemotherapy is allowed and is not counted as a line of therapy Must have received at least prior regimens of standard chemotherapy for mCRC and must have been refractory to or failed (includes intolerance to) those regimens. Prior standard chemotherapy may not have included TAS- or regorafenib, but must have included agents as specified in the protocol. Participants must have received prior platinum-based chemotherapy for management of\n primary disease but must not have received more than prior systemic cytotoxic\n regimens. Patients are allowed (but not required) to have up to two lines of prior chemotherapy regimens for metastatic disease Patients must have received at least chemotherapy regimens in the setting of metastatic disease Prior chemotherapy with - regimens is allowed Participants who have received oxaliplatin during prior systemic chemotherapy regimens are eligible for enrollment in this protocol Participants who have received oxaliplatin during prior systemic chemotherapy regimens are eligible for enrollment in this protocol Patients must have received at least one but no more than three prior systemic treatment regimens and for whom single-agent chemotherapy is appropriate as the next line of treatment Is ineligible or inappropriate for other treatment regimens known to have effective potential Disease progression after crizotinib and or prior regimens of chemotherapy in the metastatic disease setting. Patients Must have completed or previous chemotherapy regimens. Subjects must have received and have progressed, or are refractory to standard regimens Has previously received at least prior regimens for advanced disease and were refractory to or unable to tolerate their last prior therapy. At least one, but no more than three, prior chemotherapy regimens for MBC. Received and experienced disease progression on, or following one or two prior chemotherapy regimens for advanced disease. Received or more prior myelotoxic treatment regimens Patients will be ineligible if they have advanced myeloma refractory to salvage chemotherapy regimens Patients must have received less than prior chemotherapy regimens for progressive meningioma Have received prior treatment with at least chemotherapy regimens, of which at least but no more than have been administered in the metastatic setting. No more than prior chemotherapeutic regimens for metastatic disease Prior chemotherapy regimens must include a platinum and/or a fluoropyrimidine component and must not include a taxane or antiangiogenic agent. No more than three prior systemic chemotherapy regimens > prior chemotherapy regimens Subject may have received ? prior regimens for the treatment of their metastatic disease. Inclusion Criteria.\n\n - Have a diagnosis of Hormone Receptor Positive (HR+), Human Epidermal Growth Factor\n Receptor Negative (HER-) breast cancer.\n\n - Recurrent, locally advanced, unresectable or metastatic breast cancer with disease\n progression following anti-estrogen therapy.\n\n - Prior treatment with at least chemotherapy regimens:\n\n - At least of these regimens must have been administered in the metastatic\n setting.\n\n - At least of these regimens must have contained a taxane.\n\n - No more than prior chemotherapy regimens in the metastatic setting.\n\n - Have a performance status (PS) of to on the Eastern Cooperative Oncology Group\n scale.\n\n - Have discontinued all previous therapies for cancer.\n\n - Have the presence of measureable disease as defined by Response Evaluation Criteria in\n Solid Tumors Version ..\n\n Exclusion Criteria:\n\n - Have either a history of central nervous system (CNS) metastasis or evidence of CNS\n metastasis on the magnetic resonance image of brain obtained at baseline.\n\n - Received prior therapy with another cyclin-dependent kinases and (CDK/)\n inhibitor.\n\n - Have received treatment with a drug that has not received regulatory approval for any\n indication within or days of the initial dose of study drug.\n\n - Have had major surgery within days of the initial dose of study drug.\n\n - Have a history of any other cancer (except non-melanoma skin cancer or carcinoma\n in-situ of the cervix). Patients with breast cancer may have received neoadjuvant or adjuvant chemotherapy and up to two prior chemotherapy regimens for metastatic or locally recurrent disease; subjects with ovarian cancer may have had two regimens for advanced or persistent disease Patients must have had exposure to at least and no more than prior chemotherapy regimens for the treatment of metastatic breast cancer Other chemotherapy regimens may have been administered between the time of progression on prior trastuzumab containing regimen and protocol therapy; no restriction on prior chemotherapy regimens for advanced stage disease COHORT I: Patients must have received at least one and no more than two prior systemic therapy regimens; at least one of the regimens must have included pemetrexed and a platinum Participants who have received more than two prior chemotherapy regimens for metastatic CRPC More than two prior regimens for therapy of MM More than prior chemotherapy regimens; note: repeat use of regimens count as prior regimen; switching front-line therapy regimens (for example, from intraperitoneal to intravenous therapy) for reasons other than progression will count as prior therapy; bevacizumab and other targeted agents will count in the total number of prior regimens; vaccine therapies will not count in the total of prior therapies Must have had at least but no greater than prior anti-myeloma regimens. Experienced progression after one or more prior regimens of cytotoxic chemotherapy Relapsed after ? prior chemotherapy- or immunotherapy-based regimens for indolent NHL, or refractory to prior chemotherapy and/ or immunotherapy-based regimens. Patients with transformed indolent lymphoma must have received at least prior chemotherapy- and/or immunotherapy-based regimens Patients that have been treated with > prior chemotherapy regimens Patients with up to prior chemotherapy regimens are eligible Have received at least three prior chemotherapy regimens and have relapsed disease confirmed by radiologic assessment Patients who have had or more regimens containing cytotoxic chemotherapy for metastatic melanoma. Patient must have received =< prior cytotoxic regimens for metastatic breast cancer; this does not include cytotoxic regimens used in the adjuvant setting Patients with recurrent or progressive disease after one or more regimens of pre-radiation chemotherapy Prior treatment with fludarabine or alemtuzumab based regimens. More than prior Herceptin (trastuzumab) regimens or prior use of Xeloda (capecitabine) and / or Tykerb (lapatinib) [Tyverb] More than prior cytotoxic chemotherapy regimens Women with TNBC who have received at least one but no more than two prior chemotherapy regimens for TNBC Patients who have had more than prior chemotherapy regimens Patients may not have received more than prior cytotoxic regimens Prior chemotherapy regimens =< For Phase l, no more than prior anticancer regimens (IL- or interferon do not count towards the total). No more than prior regimens for DLBCL. More than prior cytotoxic chemotherapy regimens for relapsed or metastatic disease No more than prior chemotherapy regimens. Patients may not have received more than prior regimens of therapy Must have received the following treatment for glioblastoma: Prior treatment with radiotherapy and temozolomide; Note: A maximum of two prior chemotherapy/antibody regimens (including bevacizumab or other direct VEFG/VEGFR inhibitors) for recurrent disease are permitted. Prior treatment with ? prior chemotherapy-based or immunotherapy-based regimens for iNHL Subject has received more than prior cytotoxic agent-containing regimens. Radiographic progression during treatment with erlotinib; prior chemotherapy regimens are permitted Patients should have received a minimum of one, and up to five prior chemotherapy regimens More than two regimens of systemic cytotoxic chemotherapy for recurrent or advanced NSCLC Evidence of progressive disease during or following or prior chemotherapy regimens No more than prior regimens are allowed Receipt of or more prior cytotoxic chemotherapy regimens for advanced, recurrent, or metastatic endometrial cancer. Subject previously treated with chemotherapy must have no more than two prior chemotherapy regimens for the treatment of metastatic prostate cancer Patients on the phase portion of the study may not have more than prior regimens for recurrent disease for glioblastoma/gliosarcoma. Patients on the phase portion of the study may not have had more than prior regimens. Prior treatment with greater than (>) one cytotoxic chemotherapy regimens or experienced recurrent or progressive disease on > two endocrine therapies for MBC Patient received at least prior regimens for MM. More than prior cytotoxic chemotherapy regimens for recurrent or metastatic disease More than one prior chemotherapy regimens No more than two prior chemotherapy regimens for metastatic disease Patients may not have received more than prior cytotoxic regimens Have received more than prior CTX regimens No more than prior chemotherapy regimens =< prior chemotherapeutic regimens Those receiving alternate regimens and those with other disease types Have received prior chemotherapy regimens within weeks of Day ; Must be candidates for reduced-intensity conditioning regimens. Patients must also receive a full myeloablative preparative regimen (patients treated with either total body irradiation (TBI)-based or high-dose chemotherapy only regimens are eligible other than high-dose busulfan containing regimens or regimens that include anti-thymocyte globulin or other T cell depleting antibodies) Patients that are receiving or have received chemotherapy regimens are allowed Two or more prior chemotherapy regimens for advanced disease Zero or one prior chemotherapy regimens for metastatic disease At least , but no more than , prior treatment regimens for MCL Patients must have received less than three prior chemotherapy regimens for progressive meningioma At least ? prior treatment regimens for the underlying malignancy Part C: must have previously received prior treatment with at least but no more than chemotherapy regimens in the metastatic setting