Cyclophosphamide and Pulse Dexamethasone With Rapamycin or Hydroxychloroquine

Inclusion Criteria: Each subject must meet ALL of the following criteria during screening to be enrolled: * Histologically confirmed multiple myeloma * Documented relapse or persistent disease after at least one prior therapy (which may include autologous and allogeneic bone marrow transplantation) * Need for further therapy for myeloma, as determined by the patients treating physician * Age 18 years * ECOG PS 0-2 Exclusion Criteria: History of allergic reactions to compounds of similar chemical or biological composition to rapamycin or hydroxychloroquine * Patients may not take any of the following medications while on study (in the rapamycin arms only), but will be considered eligible if medication is discontinued 72 hrs prior to first dose of Rapamycin: * Carbamazepine (e.g. Tegretol) * Rifabutin (e.g. Mycobutin) * Rifampin (e.g. Rifadin) * Rifapentine (e.g. Priftin) * St. Johns Wort Clarithromycin (e.g. Biaxin) * Cyclosporin e.g. (Neorla or Sandimmune) * Diltiazem (e.g. Cardizem) * Erythromycin (e.g. Akne-Mycin, Ery-Tab) * Itraconazole (e.g. Sporonox) * Fluconazole (e.g. Diflucan) * Ketoconazole (e.g. Nizoral) * Telithromycin (e.g. Ketek) * Verapamil (e.g. Calan SR, Isoptin, Verelan) * Voriconazole (e.g. VFEND)Tacrolimus (e.g. Prograf) * Known macular degeneration or retinopathy (diabetic or otherwise), porphyria, or psoriasis (well-controlled psoriasis allowed provided under the care of a specialist who agrees to monitor the patient for exacerbations) * Patients with the following cytopenias: ANC 1.0 x 109/L; Platelets 50 x 109/L * Serum Creatinine 2.5 mg/dL; Total or Direct Bilirubin 2.0 mg/dL; Fasting Glucose 200mg/dL * Other conditions that would require therapy with hydroxychloroquine, including but not limited to, any of the following: * Systemic lupus * Rheumatoid arthritis * Porphyria cutanea tarda * Malaria treatment or prophylaxis * Other active malignancy, except: * Basal cell or squamous cell carcinoma of the skin * Treated carcinoma in situ * Localized prostate adenocarcinoma (stage T1a or T1b) with a stable PSA for a period of at least 4 months allowed * Patients with a prior malignancy treated with chemotherapy, biologic agents, and/or radiation are eligible for this study if they have completed therapy 4 years previously with no evidence of recurrent disease * Patients with a prior malignancy treated with surgery alone are eligible for this study if they have completed therapy 2 years previously with no evidence of recurrent disease * Uncontrolled intercurrent illness including, but not limited to, any of the following: * Uncontrolled ongoing infection * Symptomatic congestive heart failure * Unstable angina pectoris * Uncontrolled cardiac arrhythmia * Psychiatric illness or social situations that would limit compliance with study requirements * Inability to understand or unwillingness to sign the informed consent document * Concurrent anti-myeloma therapy within: * 7 days of prior corticosteroids * 14 days of prior antimyeloma agents, including thalidomide or lenalidomide * 28 days of a different investigational regimen * 14 days of any radiation * Women of child-bearing who are unwilling or unable to use an acceptable method to avoid pregnancy for the entire study period and for up to 30 days after the last dose of study drug. * Women who are pregnant or breastfeeding