Study of Pralatrexate to Treat Advanced or Metastatic Relapsed Transitional Cell Carcinoma of the Urinary Bladder

Inclusion Criteria: * Histologically confirmed transitional cell carcinoma of the urinary bladder. Fine needle aspirate will not be accepted. * Relapsed or progressed after treatment with a platinum- and/or methotrexate-based systemic chemotherapy regimen. No more than 1 prior regimen is permitted for recurrent/metastatic disease. Patients has had a chemotherapy-free interval of ≥ 12 months from last dose if most recent prior chemotherapy was in neoadjuvant/adjuvant setting and has had ≥ 6-month chemotherapy-free interval in recurrent/metastatic setting. Patient has recovered from the toxic effects of prior therapy. Previous intravesical therapy is allowed. Prior surgical resection is allowed, as long as the patient has recovered. * Measurable disease outside a previously irradiated region, per Response Evaluation Criteria in Solid Tumors (RECIST). * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * At least 18 years of age. * Adequate blood, liver, and kidney function as defined by laboratory results. * Patient has received 1.0-1.25 mg of oral folic acid daily for at least 7 days of enrollment \& 1 mg intramuscular vitamin B12 within 10 weeks of enrollment. * Women of childbearing potential have a negative serum pregnancy test within 14 days prior to enrollment and agree to use medically acceptable and effective birth control from enrollment until at least 30 days after the last dose of pralatrexate. * Men who are not surgically sterile and whose partner is of childbearing potential must use medically safe and effective birth control start of pralatrexate until at least 90 days after the last dose of pralatrexate. * Accessible for repeat dosing and follow up. * Give written informed consent. Exclusion Criteria: * Active concurrent primary malignancy or prior malignancies occurring within 5 years (except non-melanoma skin cancer, in situ carcinoma of the cervix, or occult, indolent carcinoma of the prostate). If there is a history of prior malignancies other than those exceptions listed above, the patient must be disease free for ≥ 5 years. Patients with other prior malignancies \< 5 years before study entry may still be enrolled if they have received treatment resulting in complete resolution of the cancer and currently have no clinical, radiologic, or laboratory evidence of active or recurrent disease. In the case of a single extrapelvic metastatic site, irrespective of the patient having a history of previous malignancy, a biopsy proof of the metastatic diseased organ will be necessary. * More than 1 previous regimen for recurrent/metastatic disease. * Evidence of clinically significant active third-space phenomenon * Use of investigational drugs, biologics, or devices within 28 days prior to study enrollment. * Previous exposure to other antifolates, including pralatrexate. Previous methotrexate is allowed, only if it was part of an M-VAC or MCV regimen. * Women who are pregnant or breastfeeding. * Congestive Heart Failure Class III/IV according to New York Heart Association (NYHA) Functional Classification. * Uncontrolled hypertension. * Human immunodeficiency virus (HIV)-positive diagnosis with a CD4 count of \< 100 mm3 or detectable viral load within the past 3 months, and receiving combination anti-retroviral therapy. * Central nervous system metastatic disease. * Major surgery within 2 weeks of study enrollment. * Radiation therapy (RT) within 4 weeks (within 3 months for RT to the pelvis) prior to study enrollment. * Active infection or any serious underlying medical condition, which would impair the ability of the patient to receive protocol treatment. * Dementia or significantly altered mental status that would prohibit the understanding and giving of informed consent or limit study compliance.