You are being asked to take part in this study because you either had Ph positive B-lineage acute lymphoblastic leukemia (ALL) or still have a small amount of the disease and recently received an allogeneic stem cell transplant (cells from someone else).

The goal of this clinical research study is to learn if blinatumomab in patients who have had an allogeneic stem cell transplant can help to control ALL or prevent ALL from coming back in patients who either have a small amount of ALL or have had ALL in the past. The safety of this drug will also be studied.

Study Drug Administration:

Every study cycle will be 6 weeks. You may receive up to 4 cycles of blinatumomab. Each cycle will start around 3, 6, 9, and 12 months after your stem cell transplant.

In each cycle, you will receive blinatumomab as a continuous infusion by vein for 4 weeks, followed by a 2 week "rest period" during which you will not receive blinatumomab.

You will need to remain in the hospital for the first 2 cycles so that you can be checked on for side effects.

Length of Study:

You may receive blinatumomab for up to 1 year. You will no longer be able to receive the study drug if the disease comes back (if you do not have ALL), if the disease gets worse (if you have a small amount of ALL), if intolerable side effects occur, or if you are unable to follow study directions.

Study Visits:

Before each cycle:

• You will have a physical exam. As part of the physical exam, you will be checked for graft versus host disease (GVHD, when transplanted donor tissue attacks the tissues of the recipient's body).
• Blood (about 4 tablespoons) will be drawn to learn the effectiveness of the stem cell transplant.
• You will have a bone marrow biopsy and aspiration to check the status of the disease and for cytogenetic testing.

Once a week during each cycle, blood (about 4 tablespoons) will be drawn for routine tests.

End of Study Visit:

About 2 weeks after your last dose of blinatumomab:

• You will have a physical exam.
• Blood (about 4 tablespoons) will be drawn to learn the effectiveness of the stem cell transplant.
• You will have a bone marrow biopsy and aspiration to check the status of the disease and for cytogenetic testing.

This is an investigational study. Blinatumomab is FDA approved and commercially available for the treatment of Philadelphia chromosome (Ph) negative B-ALL that has returned after treatment. Its use in patients with Ph positive B-lineage ALL is investigational.

Up to 30 participants will be enrolled in this study. All will take part at MD Anderson.

Inclusion Criteria:

1. Patients 1-70 years of age.
2. Patients with B-lineage ALL in a) hematologic complete remission (CR) beyond CR1 at time of transplant; patients beyond CR1 or with primary induction failure may be without minimal residual disease, b) any residual disease defined by positive flow >0.01%, detection of BCR-ABL transcript by PCR with a sensitivity of 1/10,000, or detection of the t(9;22) translocation in any metaphases by cytogenetics at time of transplant, or presence of the MLL gene.
3. Received an allogeneic HCT within the last 100 days. Enrollment within 30-100 days after transplant, and after adequate recovery of counts defined as ANC >/= 0.5 x 10^9/L without daily use of myeloid growth factor and platelet > 20 x 10^9/L without platelet transfusion within 1 week, and adequate organ function to receive blinatumomab defined as creatinine clearance greater than 30 ml/min, ALT/AST < 5 x ULN and serum bilirubin < 3 x ULN.
4. Performance status of 0, 1, or 2. Karnofsky (or Lansky for subjects < 16 years old) performance status >/= 50.

Exclusion Criteria:

1. Relapsed ALL defined as >5% malignant blasts in bone marrow or peripheral blood.
2. Active GVHD requiring systemic steroid therapy. Medications for GVHD prophylaxis are acceptable.
3. Systemic steroid therapy unless for physiologic replacement
4. Uncontrolled disease/infection as judged by the treating physician
5. Active ALL in the central nervous system (CNS), as defined by >/= 5 leukocytes per microL with identifiable blast cells in the CSF, and/or the presence of cranial-nerve palsies
6. Pregnant or nursing women