Phase I Bortezomib (VELCADE) in Combo With Pralatrexate in Relapsed/Refractory MM

Inclusion Criteria: * The patient has relapsed or refractory multiple myeloma that has progressed following at least on prior therapy. * Relapsed myeloma is defined in patients as at least 25% increasing monoclonal (M)-protein in serum or urine or in the size of a plasmacytoma compared to a best response reached after previous therapy. * Refractory myeloma is defined as failure to achieve at least a minor response (patient achieved stable disease as his/her best response) or progression of disease on current therapy or within 60 days of last dose of current therapy. * The patient has measurable disease defined as one of the following: 1. serum M-protein \>=1 g/dL 2. urine M-protein \>=200 mg/24 hours * Must have received at least one (1) prior line of systemic treatment that may have included VELCADE. a. NOTE: Patients may have undergone prior allogeneic or autologous stem cell transplantation (stem cell transplant with high dose induction chemotherapy with/without planned maintenance therapy will be considered one line of therapy). * No cytotoxic chemotherapy within 4 weeks prior to registration for protocol therapy. a. NOTE: this interval may be reduced to 14 days for thalidomide, lenalidomide, VELCADE or corticosteroids, provided other entry criteria are met. * No concurrent steroid use in doses greater than 10 mg daily of Prednisone (or equivalent) if given for management of co-morbid conditions. * Age \>= 18 at the time of consent. * The patient has a life expectancy of more than 3 months. * No known central nervous system involvement by myeloma. * ECOG performance status 0-2. * No poorly controlled intercurrent illness including, but not limited to, ongoing or active infection, poorly controlled diabetes, symptomatic congestive heart failure, or psychiatric illness that in the opinion of the investigator would limit compliance with study requirements. * Patients must have adequate bone marrow function: Platelets \>100 x 109/L, Hemoglobin \> 8.0g/dL and ANC \> 1 x 109/L * Patients must have adequate liver functions: AST and ALT \< 2.5 X upper limit of normal, Total bilirubin \<= 1.5 x ULN * Patients must have adequate renal function defined as creatinine clearance of 30 ml/minute (Cockcroft-Gault). * The patient must have been on a regimen of 1.0 - 1.25 mg PO QD of folic acid for at least 10 days prior to the planned start of pralatrexate and received 1 mg IM of vitamin B12 within 10 weeks of the planned start of pralatrexate. * Patients with reproductive potential must use an effective method of contraception to avoid pregnancy for the duration of the trial. * If female of childbearing potential, pregnancy test must be negative within 7 days prior to registration for protocol therapy. * Ability to understand and the willingness to sign a written informed consent document including HIPAA authorization for release of personal health information. * The patient must be willing and able to receive outpatient treatment and laboratory monitoring at the Stanford Cancer Center. Exclusion Criteria: * The patient has nonmeasurable multiple myeloma, defined as less than 1g/dl M-protein in serum and less than 200 mg/24 hours M-protein in urine. * The patient received glucocorticoid therapy (prednisone \> 10 mg/day orally or equivalent) within the last 2 weeks prior to the first dose of study drug. * The patient received chemotherapy with approved or investigative anticancer therapeutics within 4 weeks. a. NOTE: this interval may be reduced to 14 days for thalidomide, lenalidomide, VELCADE or corticosteroids, provided other entry criteria are met. * The patient has an acute infection requiring systemic antibiotics, antiviral agents, or antifungal agents within 2 weeks before the first dose of study drug. * The patient has grade 2 or higher neuropathy within 14 days of enrollment. * The patient has any serious psychiatric or medical condition that could interfere with treatment and study procedures, place the patient at unacceptable risk, or confound the ability of investigators to interpret study data. * The patient is a pregnant or lactating woman. * Myocardial infarction within 6 months prior to enrollment or has New York Heart Association (NYHA) Class III or IV heart failure (see Appendix A), uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality at Screening has to be documented by the Investigator as not medically relevant. * Patient has hypersensitivity to VELCADE, boron or mannitol. * Diagnosed or treated for another malignancy within 3 years of enrollment, with the exception of complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, an in situ malignancy, or low-risk prostate cancer after curative therapy.