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.