Combination Therapy (Mirdametinib and Sirolimus) for RAS Mutated Relapsed Refractory Multiple Myeloma

Background: Multiple myeloma (MM) is a type of blood cancer that affects a person s immunity. MM returns after treatment (relapse) in almost all people; MM may also not respond to initial treatment (refractory). Many people with relapsed refractory MM (RRMM) also have changes in their KRAS and NRAS genes. Researchers want to try a new drug treatment that targets cancer with these changed genes. Objective: To test 2 drugs (mirdametinib and sirolimus) in people with RRMM. Eligibility: People aged 18 and older with RRMM who have changes in their KRAS or NRAS genes. Design: Participants will be screened. They will have blood tests and imaging scans. They will have an eye exam and a test of their heart function. They will need to provide proof of their disease status and of their KRAS or NRAS status. If neither is available, the tests will be repeated. Participants will have a bone marrow biopsy: A needle will be inserted into a hipbone to draw out some soft tissue. This study will be done in two parts. In the first part of this study, we will find a safe dose of mirdametinib combined with sirolimus. In the second part, we will learn more about how mirdametinib combined with sirolimus may work against RRMM. Mirdametinib (capsules) and sirolimus (tablets) are taken by mouth. Participants will take both drugs at home on a 4-week cycle. They will take mirdametinib twice a day for the first 3 weeks of each cycle. They will take sirolimus once a day, every day, during each cycle. Participants will have study visits once a week during the first cycle, and then on the first day of subsequent cycles. Blood, heart, imaging scans, and other tests will be repeated. Treatment with the study drugs will go on for 1 year. Then participants will have follow-up visits every 3 months for 4 more years.

* INCLUSION CRITERIA: * Participants must have a documented diagnosis of multiple myeloma (MM) defined by the International Myeloma Working Group (IMWG) Criteria. Participants at diagnosis must have had a history of the serum-M protein \>= 3 g/dL and or bone marrow plasma cells \>= 10% and the history of at least one of the following: * Anemia: hemoglobin \= 11 mg/dL OR \> 1 mg/dL higher than the upper limit of normal (ULN), OR * Lytic bone lesions on X-Ray, Computed Tomography (CT), or Positron Emission Tomography (PET)/CT, OR * \>= 2 focal lesions on spinal Magnetic Resonance Imaging (MRI), OR * \>= 60% bone marrow plasma cells, OR * Involved/un-involved serum-free light chain ratio \>= 100. * Participants must have measurable disease per International Myeloma Working Group (IMWG) criteria. * Participants must have relapsed and/or refractory multiple myeloma (RRMM) with "penta-class exposed" disease, as defined by previous therapy with an anti-CD38 monoclonal antibody, 2 immunomodulatory drugs \[IMiDs\], and 2 proteasome inhibitors \[Pis\]), 3 previous lines of therapy, and no other available options. * Participants must have a history of known somatic mutation in KRAS or NRAS. Note: For participants that come to NIH without confirmation of KRAS or NRAS, their status will be determined by the TSO500 NSR device. * Participants must be off other myeloma-directed therapy (except for radiation) for at least 14 days prior to the study treatment initiation. * Age \>= 18 years. * ECOG performance status \= 1,000 cells/microliter Platelets: \>= 75,000 cells/microliter Total bilirubin: within normal institutional limits Aspartate Aminotransferase (AST): \ 160 mm Hg) and/or uncontrolled diabetes mellitus type II (DMII) (chronic clinical signs/symptoms of hyperglycemia; diabetic participants must have a hemoglobin A1c value \< 9% to be eligible). * Participants receiving systemic or ocular glucocorticoid therapy equivalent to \> 10 mg of prednisone daily within 14 days prior to the study treatment initiation. Note: Participants with endocrine deficiencies, who receive physiologic, or stress doses of steroids are eligible. * Participants receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 within 14 days prior to the study treatment initiation. Lists including medications and substances known or with the potential to interact with the CYP3A4 isoenzymes are provided here: http://medicine.iupui.edu/clinpharm/ddis/table.aspx. * Participants receiving any medications or substances that are strong inhibitors of breast cancer resistance protein (BCRP) within 14 days prior to the study treatment initiation (i.e., curcumin, cyclosporine, darolutamide, eltrombopag, febuxostat, fostamatinib, rolapitant, sofosbuvir and velpatasvir and voxilaprevir, and teriflunomide). * Positive beta-human chorionic gonadotropin (beta-HCG) serum or urine pregnancy test performed in IOCBP at screening. * Participant has abnormal QT interval corrected by Fridericia s formula (QTcF \>470 ms, as determined by the mean QTcF values from the ECG assessments at screening (one triplicate). * Uncontrolled intercurrent illness or factors evaluated by medical history and physical exam that would potentially increase the risk of the participant.