Selinexor (KPT-330) and Liposomal Doxorubicin For Relapsed and Refractory Multiple Myeloma

Inclusion Criteria: * Patients with relapsed and refractory multiple myeloma who have received at least 2 prior therapies which must include lenalidomide and a proteasome inhibitor. Patients must have disease refractory to the most recent therapy. Refractory myeloma is defined as progressive disease during or within 60 days of last therapy. Patients must have previously received or be ineligible for (or refused) autologous stem cell transplant. * Must have measurable myeloma paraprotein levels in serum (≥ 0.5 g/dL) or urine (≥ 0.2 g excreted in a 24-hour urine collection sample) or by free light chain (involved free light chain greater than 100 mg/L). * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. ECOG 2 allowed if due to bone disease * Must have an echocardiogram or multigated acquisition (MUGA) scan indicating left ventricular ejection fraction (LVEF) ≥ 50% within 42 days prior to first dose of study drug * Adequate hematological function * Adequate hepatic function within 14 days prior to loading phase (day -14) * Adequate renal function within 14 days prior to loading: estimated creatinine clearance of ≥ 30 mL/min, (Cockcroft and Gault) * Female patients of child-bearing potential must agree to use dual methods of contraception and have a negative serum pregnancy test at screening. Male patients must use an effective barrier method of contraception if sexually active with a female of child-bearing potential. For both male and female patients, effective methods of contraception must be used throughout the study and for three months following the last dose. Exclusion Criteria: * Women who are pregnant or lactating * Radiation, chemotherapy, or immunotherapy or any other approved anticancer therapy ≤2 weeks prior to day -7 (beginning of loading phase) * Major surgery within four weeks before Day -7 * Myocardial infarct within 6 months before enrollment, New York Heart Association (NYHA) Class II or greater heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, clinically significant pericardial disease, or electrocardiographic evidence of acute ischemic or active conduction system abnormalities * Prior cumulative exposure to doxorubicin (including liposomal preparation) \> 350mg/m\^2 * Uncontrolled infection requiring parenteral antibiotics, antivirals, or antifungals within one week prior to first dose; patients with controlled infection or on prophylactic antibiotics are permitted in the study * Known to be HIV seropositive * Known active hepatitis A, B, or C infection; or known to be positive for hepatitis C virus (HCV) RNA or HBsAg (HBV surface antigen) * Any underlying condition that would significantly interfere with the absorption of an oral medication * Grade \>2 peripheral neuropathy at baseline (within 14 days prior to loading phase (day -7)) * Serious psychiatric or medical conditions that could interfere with treatment * Participation in an investigational anti-cancer study within 3 weeks prior to day -7(beginning of loading phase) * Concurrent therapy with approved or investigational anticancer therapeutic * Coagulation problems and active bleeding in the last month * Previous allogeneic transplant within 6 months and have evidence of clinically significant graft versus host disease