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

* 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 \<= 10 g/dL or a 2g/dL decrease from the lower limit of normal, OR * Renal failure: creatinine clearance \< 40 ml/min, OR * Hypercalcemia: calcium (Ca) \>= 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 \<= 2. * Participants must have adequate organ and marrow function as defined below: Absolute neutrophil count (ANC): \>= 1,000 cells/microliter Platelets: \>= 75,000 cells/microliter Total bilirubin: within normal institutional limits Aspartate Aminotransferase (AST): \<= 3 X ULN Alanine Aminotransferase (ALT): \<= 3 X ULN Renal function: creatinine clearance (CrCl) \>= 40 mL/min calculated by Cockcroft-Gault, -Individuals of childbearing potential (IOCBP) must agree to use highly effective contraception (hormonal, intrauterine device \[IUD\], abstinence, surgical sterilization) at the study entry and for at least 12 weeks after the last dose of sirolimus or 6 months after the last dose of mirdametinib, whichever is longer. Barrier methods such as condoms (male or female) or occlusive caps (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream or vaginal suppository must be used in addition to hormonal contraception. Note: IOCBP is defined as any individual who has experienced menarche and who has not undergone successful surgical sterilization or who is not postmenopausal. Individuals able to father a child must agree to use an effective method of contraception (barrier plus spermicide, surgical sterilization, abstinence) at the study entry and for 3 months after the last dose of mirdametinib. We also will recommend individuals able to father a child with partners of childbearing potential ask partners to be on highly effective birth control (hormonal, IUD, surgical sterilization) for at least 3 months after the last dose of mirdametinib. Individuals able to father a child must not freeze or donate sperm within the same period. * Breastfeeding participants must be willing to discontinue breastfeeding after study treatment initiation. * Participants seropositive for human immunodeficiency virus (HIV) infection must: * be on anti-retroviral therapy; and * have the undetectable viral load. * Participants seropositive for Hepatitis C virus (HCV) infection must * have been treated and cured; or * if currently on treatment, have an undetectable HCV viral load. * Participants seropositive for Hepatitis B virus (HBV) infection must * be on suppressive therapy if necessary; and * have viral load \<100 IU/mL. * Ability of the participant to understand and the willingness to sign a written informed consent document. EXCLUSION CRITERIA: * Received any investigational agents within 14 days prior to the study treatment initiation. * Vaccinated with live, attenuated vaccines within 30 days prior to the study treatment initiation. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to mirdametinib and/or sirolimus. * Current diagnosis of plasma cell leukemia. * Current or history of amyloidosis. * Current or history of New York Heart Association (NYHA) Stage III or IV heart failure * Current or history of Interstitial Lung Disease. * Current or history of glaucoma and/or an intraocular pressure \> 22 mmHg, retinal pigment epithelial detachment, or other primary ocular/retinal diseases. * Current or history of retinal vein occlusion (RVO). * Comorbidities that put undue risk of RVO such as uncontrolled hypertension (chronic systolic blood pressures \> 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.