Histologically confirmed diagnosis of symptomatic multiple myeloma; relapsed disease is myeloma that has previously responded to prior therapy (MR or better) and subsequently progressed Participant has received previous multiple myeloma treatment as defined in the protocol for Part 1 and Part 2 of this study. Males or females with multiple myeloma who have exhausted available standard therapies. Anti-myeloma treatment within 2 weeks Participants must have relapsed or refractory (R/R) multiple myeloma (MM) for which no established therapy for MM is appropriate and available or be intolerant to those established therapies Patients with relapse/ refractory multiple myeloma Histologically confirmed Multiple Myeloma prior to enrolment and randomization. Histologically confirmed diagnosis of secretory multiple myeloma (must have measurable M protein in serum or urine) with at least one of the following: A prior diagnosis of multiple myeloma with documented disease progression requiring further treatment at time of screening Hematologic malignancies (including lymphoma, multiple myeloma) Patients must have a confirmed biopsy diagnosis of a multiple myeloma Diagnosis of multiple myeloma (MM) and documentation of treatment Histologically or cytologically confirmed multiple myeloma Myeloma specific therapy with a minimum of 3 cycles Cytopathologically or histologically confirmed dx of multiple myeloma Any prior therapy for symptomatic multiple myeloma or smoldering multiple myeloma should also be excluded, including prior use of IMIDs, proteasome inhibitors, or CD138 inhibitors; prior therapy for smoldering multiple myeloma with agents that are not therapeutically active against MM is not an exclusion criterion Is in need of additional myeloma therapy as determined by the investigator. Patients with high risk multiple myeloma (criterion 3a above) in very good partial response (VGPR) or better at the time of enrollment with at most 1 prior progression within 18 months from initiation of systemic anti-myeloma therapy, which may include single or planned tandem autologous HSCT; or Patients with standard risk multiple myeloma in VGPR or better at the time of enrollment with 1 prior progression within 18 months from a single or planned tandem autologous HSCT; or IgA, IgD, IgE, IgM multiple myeloma: serum M-protein level ?0.5 g/dL (measured by PEP). multiple myeloma Multiple myeloma that has relapsed after, or was not responsive to, initial therapy. Symptomatic multiple myeloma, International Staging System (ISS) stages I-III, within 12 months of starting therapy COHORT A: multiple myeloma Prior cytotoxic chemotherapy or corticosteroids for the treatment of multiple myeloma; NOTE: prior corticosteroid use for the treatment of non-malignant disorders is permitted Multiple myeloma beyond PR2: Patients with chromosome 13 abnormalities, first response lasting less than 6 months, or beta-2 microglobulin > 3 mg/L, may be considered for this protocol after initial therapy Relapsed or refractory hematologic malignancy (lymphoma or multiple myeloma) that has progressed, or is currently progressing with standard anticancer therapy or for which no other approved therapy exist. Lymphoma patients must have failed at least 2 standard anticancer therapies, and multiple myeloma patients must have failed at least 3 standard anticancer therapies. Received systemic treatment for multiple myeloma, including immunotherapy, within 14 days prior to initiation of study procedures Myeloma disease that is refractory to ixazomib treatment A prior diagnosis of multiple myeloma with documented disease progression in need of treatment at time of screening Pathologically confirmed diagnosis of multiple myeloma who are transplant eligible and have received any prior induction therapy (with or without maintenance) Any previous ASCT for multiple myeloma (MM) Patients with multiple myeloma in first relapse (or who are primary refractory) following treatment with a bortezomib-containing regimen (excluding prior treatment with ixazomib) Participants with measurable multiple myeloma who have progressed on, or could not tolerate, all available established therapies Patients must meet the criteria for symptomatic multiple myeloma prior to initiating systemic anti-myeloma treatment. Documented multiple myeloma as defined by the criteria below: International Staging System (ISS) stage I-III multiple myeloma that has progressive, relapsed, or refractory disease Smoldering (asymptomatic) multiple myeloma Histologically- or cytologically-confirmed relapsed or refractory multiple myeloma (MM) with measurable disease Multiple myeloma, solitary plasmacytoma, or primary malignant lesions in the index vertebra or bone Diagnosis of newly diagnosed multiple myeloma with indication for initiation of therapy Measurable multiple myeloma that is relapsed or refractory to established therapies with known clinical benefit in relapsed/refractory multiple myeloma or be intolerant of those established multiple myeloma therapies, and a candidate for JNJ-64007957 treatment in the opinion of the treating physician. Prior lines of therapy must include a proteasome inhibitor and an immunomodulatory drug in any order during the course of treatment. Participants who could not tolerate a proteasome inhibitor or immunomodulatory drugs are allowed Histologically confirmed diagnosis of multiple myeloma Diagnosis\r\n* Phase I: confirmed diagnosis of relapsed or refractory multiple myeloma\r\n* Phase II: confirmed diagnosis of active multiple myeloma and must be newly diagnosed\r\n* NOTE: all tests for establishing disease status must be completed =< 28 days prior to registration Relapsed multiple myeloma that is chemotherapy sensitive and has failed or ineligible for an autologous transplant Prior or concurrent systemic treatment for SMM; b) bisphosphonates are permitted, including pamidronate, zoledronic acid, alendronate, ibandronate, risedronate; c) treatment with corticosteroids is not permitted, unless the patient is on a stable chronic dose of inhaled steroids to treat respiratory diseases or on stable chronic steroid replacement therapy for endocrinology disorders; d) radiotherapy is not permitted, e) prior treatment for smoldering multiple myeloma with chemotherapy agents approved for the treatment of multiple myeloma or CD38 drugs is not permitted Histologic and serologic findings, reviewed at Memorial Sloan Kettering Cancer Center (MSKCC), confirming the diagnosis of multiple myeloma or AL amyloidosis; standard diagnostic criteria for multiple myeloma will be used, as per the International Myeloma Foundation consensus guidelines At time of enrollment, subjects must be within 9 months of initiation of systemic therapy for multiple myeloma Patients with histologically confirmed multiple myeloma Non-secretory multiple myeloma Multiple myeloma: stage II or III, symptomatic, secretory multiple myeloma requiring treatment RESEARCH SAMPLE COLLECTION: Histologically confirmed diagnosis of multiple myeloma Histologically confirmed diagnosis of multiple myeloma Relapsed multiple myeloma that is chemotherapy sensitive and has failed or ineligible for an autologous transplant Patient must have relapsed and symptomatic multiple myeloma Patients who have received > 3 prior treatment regimens for multiple myeloma Multiple myeloma beyond PR2: Patients with chromosome 13 abnormalities, first response lasting less than 6 months, or beta-2 microglobulin > 3 mg/L, may be considered for this protocol after initial therapy Multiple myeloma progressive on salvage chemotherapy Multiple myeloma specific:\r\n* Confirmed evidence of disease progression from immediately prior multiple myeloma (MM) therapy or refractory to the immediately prior treatment\r\n* Measurable disease M protein component in serum (at least 0.5 g/dL) and/or urine (if present), (>=0.2 g excreted in a 24 hour collection sample)\r\n* Subjects with free light chain only disease are excluded Histologically confirmed diagnosis of symptomatic multiple myeloma; (patients with multiple myeloma with secondary amyloidosis are eligible) Received at least two cycles of any regimen as initial systemic therapy for multiple myeloma and are within 2-16 months of the first dose of initial therapy Administration or planned administration of any other concomitant chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy which would be considered a treatment of multiple myeloma until day +28 post-transplant through discontinuation from study; patients may be on corticosteroids if they are being given for disorders other than multiple myeloma (e.g., adrenal insufficiency, rheumatoid arthritis, etc.) Non-secretory multiple myeloma Recent history of other (non multiple myeloma) cancer Patients must have a diagnosis of multiple myeloma Multiple myeloma\r\n* Relapse/progression after autologous HSCT\r\n* Plasma cell leukemia\r\n* Adverse cytogenetics: e.g. del(13q) or 11q translocation\r\n* At the time of enrollment, multiple myeloma (MM) must be in complete remission Diagnosis of symptomatic multiple myeloma (MM) Cytopathologically or histologically confirmed diagnosis of multiple myeloma Recipients must have histopathologically confirmed diagnosis of multiple myeloma Multiple myeloma beyond PR2; patients with chromosome 13 abnormalities, first response lasting less than 6 months, or beta-2 microglobulin > 3 mg/L, may be considered for this protocol after initial therapy Multiple myeloma beyond PR2: Patients with chromosome 13 abnormalities, first response lasting less than 6 months, or beta-2 microglobulin > 3 mg/L, may be considered for this protocol after initial therapy Patients must have one of the following diagnoses of multiple myeloma (MM) or primary/secondary myelofibrosis (MF) Patients must have a known diagnosis of multiple myeloma with evidence of measurable disease, as defined below: Criteria 1 Relapsed or progressive multiple myeloma after last treatment IgG multiple myeloma: serum monoclonal paraprotein (M-protein) level IgA, IgD, IgE multiple myeloma: serum M-protein level ? 0.5 g/dL, Criteria 2 Multiple myeloma of IgM subtype Subject has histologically confirmed multiple myeloma that has never before been treated Subject has previously been treated for multiple myeloma Relapsed/refractory multiple myeloma with progressive disease at study entry Patient received chemotherapy or other anti-cancer therapy that may be active against multiple myeloma within 3 weeks prior to the first dose of PRLX 93936. Patient is taking any therapy concomitantly that may be active against multiple myeloma. Multiple myeloma: stage II or III, symptomatic, secretory multiple myeloma requiring treatment Patient with confirmed multiple myeloma requiring systemic therapy. All three criteria must be met: Patient whose disease progressed during or within 60 days of bortezomib treatment or of any other Multiple Myeloma therapy Confirmed relapsed or refractory multiple myeloma after at least two prior lines of therapy. Multiple myeloma (Eligible patients must have quantifiable M-protein levels present in serum and/or urine) Progressive disease must have occurred either during or subsequent to the patient's last treatment for multiple myeloma prior to the current enrollment Patient must have substantially recovered from clinically significant toxicities from prior therapies for multiple myeloma Multiple myeloma with IgM subtype Histologically confirmed diagnosis of multiple myeloma; (patients with multiple myeloma with secondary amyloidosis are eligible) Received at least two cycles of any regimen as initial systemic therapy for multiple myeloma and are within 2-13 months of the first dose of initial therapy Evidence of multiple myeloma (MM) disease progression any time prior to enrollment; progression from smoldering to active myeloma is not exclusionary Patients with multiple myeloma in complete response (CR), partial remission (PR), very good partial remission (VGPR), or symptomatic stable disease (no evidence of progression) including patients with light chain multiple myeloma (MM) detected in the serum by free light chain assay. Relapsed or refractory multiple myeloma. Participants with primary refractory myeloma only allowed in dose-escalation phase of the study. For expansion cohorts only: Primary refractory multiple myeloma defined as disease that is non-responsive in participants who have never achieved a minimal response or better with any therapy Subjects must have histologically confirmed diagnosis of multiple myeloma Planned concurrent treatment for multiple myeloma other than bisphosphonates Diagnosis of multiple myeloma according to International Myeloma Working Group criteria and one of the following:\r\n* Smoldering multiple myeloma (SMM)\r\n* Indolent multiple myeloma (IMM)\r\n* Newly diagnosed multiple myeloma (MM)\r\n* Note: patients with lytic disease and anemia are eligible Patients must meet established criteria for the diagnosis of multiple myeloma Patients with non-secretory multiple myeloma are not eligible Prior cytotoxic chemotherapy or corticosteroids for the treatment of multiple myeloma\r\n* NOTE: Prior corticosteroid use for the treatment of non-malignant disorders is permitted FOR PATIENTS WITH MULTIPLE MYELOMA (MM): Diagnosis of multiple myeloma Symptomatic multiple myeloma requiring treatment Received at least two cycles of any regimen as initial systemic therapy for multiple myeloma and are within 2-12 months of the first dose of initial therapy Smoldering multiple myeloma (MM) not requiring therapy Multiple myeloma progressive on salvage chemotherapy Histologically confirmed diagnosis of multiple myeloma Received at least two cycles of any regimen as initial systemic therapy for multiple myeloma and are within 2-12 months of the first dose of initial therapy MULTIPLE MYELOMA CRITERIA: Patients must have received at least 3 different prior treatment regimens for multiple myeloma Patients must have histologically or cytologically confirmed multiple myeloma not otherwise specified (NOS) (10028566) A diagnosis of multiple myeloma (MM) and documentation of relapsed or relapse/refractory status following at least 2 prior lines of therapy Patients must have a confirmed diagnosis of symptomatic multiple myeloma and must be currently relapsed or refractory; except where otherwise indicated below that assessment is required within 14 days, all tests for establishing disease status must be completed within 28 days prior to registration and documented on the Baseline Tumor Assessment Form for Multiple Myeloma Any chemotherapy, immunotherapy, biologic, investigational, for treatment of multiple myeloma other than lenalidomide and dexamethasone Diagnosis of non-secretory myeloma MULTIPLE MYELOMA CRITERIA Prior glucocorticosteroid therapy for the treatment of multiple myeloma is not permitted Confirmed diagnosis of active multiple myeloma and measurable disease. Has non-secretory multiple myeloma Has a confirmed diagnosis of active multiple myeloma and measurable disease multiple myeloma (MM) - Documented relapsed or progressive Multiple Myeloma (MM) on or after any regimen or is refractory to the most recent line of therapy. Any one or more of the following myeloma defining events: Has a confirmed diagnosis of active multiple myeloma and measurable disease. Has non-secretory or oligosecretory multiple myeloma Pathologically documented,multiple myeloma relapsed or refractory progressive disease after at least 3 lines of therapy for multiple myeloma. Prior therapeutic treatment or regimens must include proteasome inhibitors (e.g. bortezomib) and immunomodulatory drugs (e.g. lenalidomide). Multiple myeloma with IgM subtype Confirmed diagnosis of symptomatic multiple myeloma and measurable secretory disease For Multiple Myeloma cohort Have a documented diagnosis of multiple myeloma and have relapsed and refractory disease. Primary refractory multiple myeloma defined as patients who have never achieved at least a minimal response (MR) with any treatment during the disease course. Participant has documented relapsed or progressive multiple myeloma on or after any regimen or who are refractory to the most recent line of therapy. Relapsed myeloma is defined as previously treated myeloma that progresses and requires initiation of salvage therapy, but does not meet the criteria for refractory myeloma. Refractory myeloma is defined as disease that is non responsive (failure to achieve minimal response or development of progressive disease [PD]) while on primary or salvage therapy, or progresses within 60 days of last therapy. Histologically confirmed multiple myeloma Four or less prior lines of systemic therapy for multiple myeloma Newly diagnosed or relapsed multiple myeloma For newly diagnosed multiple myeloma: multiple myeloma of IgM subtype Diagnosis of smoldering multiple myeloma (SMM) for less than 5 years Active multiple myeloma,requiring treatment as defined by the study protocol Must have had documented multiple myeloma Must have received at least 1 prior line of therapy for multiple myeloma Has a history of malignancy (other than multiple myeloma) within 3 years before the date of randomization Subjects of ? 18 years of age with histopathologically confirmed diagnosis of lymphoma or multiple myeloma that is refractory to or relapsed after at least 2 prior regimens. Documented measurable disease for multiple myeloma at screening as defined in protocol Prior or concurrent systemic treatment for SMM; a) bisphosphonates are permitted; b) treatment with corticosteroids is not permitted; c) radiotherapy is not permitted; d) prior treatment for smoldering multiple myeloma with chemotherapy agents approved for the treatment of multiple myeloma is not permitted Relapsed multiple myeloma Refractory multiple myeloma defined as meeting 1 or more of the following: At least 2 but no more than 3 prior therapies for multiple myeloma Multiple myeloma of Immunoglobin M (IgM) subtype New diagnosis of multiple myeloma with no prior history of treatment (exceptions include corticosteroids, bisphosphonates, single agent cyclophosphamide, =< 21 days of the first cycle of a planned regimen) Patient has exquisitely radiosensitive histology, such as multiple myeloma, lymphoma, leukemia, or seminoma Must have documented multiple myeloma and measurable disease Must have received at least 1 prior line of therapy for multiple myeloma and achieved a response (partial response or better) to at least one prior regimen Histologic confirmation of multiple myeloma by the enrolling institution Patients with a diagnosis of multiple myeloma (MM) not achieving a VGPR or better to the most recent therapy. Patients receiving > 1 cycle of prior treatment or concurrent systemic treatment for multiple myeloma\r\n* Treatment of hypercalcemia or spinal cord compression or aggressively progressing myeloma with current or prior corticosteroids is permitted\r\n* Bisphosphonates are permitted\r\n* Concurrent or prior treatment with corticosteroids for indications other than multiple myeloma is permitted\r\n* Prior treatment with radiotherapy is permitted\r\n* Prior treatment for smoldering myeloma is permitted with a washout period of 2 weeks from last dose; smoldering patients previously treated with carfilzomib are excluded\r\n* Patients with measurable disease who received up to one cycle of any therapy within 60 days with a washout period of 2 weeks from last dose (on a trial or outside a trial) are eligible Relapsed or refractory multiple myeloma and has already received =< 4 standard treatment regimens; note: induction, transplant, consolidation, and maintenance is considered one regimen Prior treatment for multiple myeloma with either standard of care treatment or investigational regimen Diagnosis of multiple myeloma with measureable disease Patients requiring therapy who have relapsed and/or are refractory to their last therapy and have been treated with at least 1, but not more than 5 lines of multiple myeloma therapy. Must have documented diagnosis of multiple myeloma and have measureable disease by serum and urine protein electrophoresis. Non-secretory multiple myeloma. Symptomatic multiple myeloma; (Part 1) Have relapsed multiple myeloma after receiving a minimum of 2 and a maximum of 4 prior lines of therapy and be eligible for treatment with lenalidomide and dexamethasone (Len/Dex) (Part 2) Have received at least 1 prior line of therapy for multiple myeloma Recovered from the effects of any prior systemic therapy or radiotherapy for Multiple Myeloma Diagnosis of smoldering multiple myeloma (SMM) for <4 years Confirmed diagnosis of multiple myeloma that is relapsed and/or refractory for which no curative option exists. Patient must not have been previously treated with any prior systemic therapy for the treatment of active multiple myeloma\r\n* Prior treatment of hypercalcemia or spinal cord compression with corticosteroids does not disqualify the patient (the dose should not exceed the equivalent of 320 mg of dexamethasone in a 2 week period)\r\n* Bisphosphonates are permitted\r\n* Prior therapy for smoldering myeloma is permitted Patients with relapsed multiple myeloma who have already received one or more standard treatment regimens Previously diagnosed with multiple myeloma. A histologically established diagnosis of multiple myeloma with evidence of relapse or refractory disease. Refractory or relapsed multiple myeloma Confirmed diagnosis of multiple myeloma Patient must have multiple myeloma that has either relapsed or has high risk cytogenetics Patients receiving > 1 cycle of prior treatment or concurrent systemic treatment for multiple myeloma\r\n* Treatment of hypercalcemia or spinal cord compression or aggressively progressing myeloma with current or prior corticosteroids is permitted\r\n* Bisphosphonates are permitted\r\n* Concurrent or prior treatment with corticosteroids for indications other than multiple myeloma is permitted\r\n* Prior treatment with radiotherapy is permitted\r\n* Prior treatment for smoldering myeloma is permitted with a washout period of 4 weeks from last dose; smoldering patients previously treated with carfilzomib are excluded\r\n* Patients with measurable disease who received up to one cycle of any therapy within 60 days with a washout period of 4 weeks from last dose (on a trial or outside a trial) are eligible Must have received 1-5 prior therapies for their myeloma and have relapsed or refractory multiple myeloma; prior therapy with bortezomib is allowed as long as they were not refractory to bortezomib Patients may have received 1 cycle of prior therapy with dexamethasone for multiple myeloma Multiple myeloma\r\n* Relapse/progression after autologous HSCT\r\n* Plasma cell leukemia\r\n* Adverse cytogenetics: del(13q) or 11q translocation Multiple myeloma: stage II or III, symptomatic, secretory multiple myeloma requiring treatment Lesions due to hematologic malignancy (e.g. multiple myeloma at site of the index vertebra (e), Diagnosed with previously treated multiple myeloma. Histologically or cytologically confirmed diagnosis of multiple myeloma that has progressed despite at least one line of standard therapy Treatment Group C (TGC): Multiple myeloma Confirmed diagnosis of multiple myeloma with a BRAF V600 mutation Must have received at least one prior systemic therapy for the treatment of multiple myeloma Must have relapsed and/or refractory multiple myeloma with measurable disease Melanoma, papillary thyroid cancer or hematological malignancies (with the exception of multiple myeloma) Patients previously diagnosed with multiple myeloma Diagnosis of multiple myeloma No more than six months’ worth of multiple myeloma chemotherapy is allowed (from the date of the start of the induction therapy) Diagnosis of relapsed multiple myeloma Patients with confirmed multiple myeloma whose treatment history must include all of the following: Patients with relapsed/refractory multiple myeloma based on standard criteria Confirmed multiple myeloma with measurable disease. Patients with any hematologic malignancy. This includes leukemia (any form), lymphoma, and multiple myeloma. Patients with relapsed/refractory multiple myeloma after at least 1 prior therapy No prior treatment for multiple myeloma Multiple myeloma of IgM (immunoglobulin M) subtype Multiple myeloma Relapsed or refractory Multiple Myeloma (MM) a. Treated with at least 1 prior regimen for myeloma Patients with relapsed multiple myeloma who have already received one or more standard treatment regimens Multiple myeloma with relapsing or progressing disease at study entry. Patients must have evaluable multiple myeloma with, at least one of the following (assessed within 21 days prior to randomization): Multiple Myeloma of IgM subtype. Diagnosis of relapsed or refractory multiple myeloma (MM) and documentation of at least 1 prior therapy; there is no maximum number of prior regimens Multiple myeloma (MM) Subjects with Multiple Myeloma (MM) and renal function fitting one of three categories: Prior systemic therapy for multiple myeloma, including investigational drugs (prior treatment with corticosteroids or localized radiation therapy dose not disqualify the patient) Has prior systemic therapy for multiple myeloma, including investigational drugs (prior treatment with corticosteroids or localized radiation therapy dose not disqualify the participantt) Subjects must have documented diagnosis of multiple myeloma and have measurable disease Use of any anti-myeloma drug therapy within 14 days of initiation of study drug treatment excluding corticosteroids if given for an indication other than myeloma; note: bisphosphonates are not considered anti-myeloma drugs Relapsed multiple myeloma. At least ?1 line of therapy and progressed after ?1 prior therapy Symptomatic multiple myeloma Prior treatment with at least one, but no more than three, regimens for multiple myeloma Age 18 years or older with a confirmed diagnosis of multiple myeloma (MM) and documentation of one to three prior therapies. Patients must have a diagnosis of active multiple myeloma Patients who have not received any chemotherapy treatment for multiple myeloma prior to being enrolled in the study Patients who were receiving simvastatin (dose > 40 mg/day) while receiving current chemotherapy regimen for multiple myeloma Multiple myeloma that does not express M-protein or FLC (i.e., non-secretory MM is excluded), and quantitative immunoglobulin levels cannot be used instead. Participants must have histologically confirmed multiple myeloma that is relapsed or refractory Patients may have had 1 or more prior chemotherapy regimens for multiple myeloma but none within the preceding 14 days Diagnosis of cancer, not including multiple myeloma or lymphoma/leukemia Diagnosis of multiple myeloma Documented evidence of multiple myeloma (per local assessment): Diagnosis of multiple myeloma High risk, or refractory and relapsed multiple myeloma Multiple myeloma (MM), requiring treatment, defined by any of the following: Pathologically-documented diagnosis of multiple myeloma that is relapsed or is refractory as defined by the following: Multiple myeloma with IgM subtype Subject has aplastic anemia or multiple myeloma Histologically confirmed multiple myeloma (newly diagnosed or relapsed); (Note: multiple myeloma patients with secondary amyloidosis are eligible) Patients with the clinical diagnosis of multiple myeloma (MM) will be referred to MRI by hematologists/oncologists at New York University Medical Center (NYUMC) who care for these patients A prior diagnosis of multiple myeloma with documented disease progression Subject must have a pathologically documented, definitively diagnosed, multiple myeloma relapsed, or refractory progressive disease after at least 2 lines of therapy for multiple myeloma. Prior therapeutic treatment or regimens must include a proteasome inhibitor and lenalidomide. Multiple myeloma with IgM subtype. Have history of paraproteinemias or multiple myeloma Relapsed multiple myeloma Received at least 1 prior treatment regimen or line of therapy for multiple myeloma Immunoglobulin M (IgM) multiple myeloma Previous treatments for multiple myeloma (MM) within 2 weeks of initiation of study treatment Hematologic malignancies or multiple myeloma.