This research study is a Phase I clinical trial. Phase I trials test the safety of an investigational drug or combination of drugs. These trials also try to define the appropriate dose of the investigational drug to use for further studies. "Investigational" means that the combination of drugs is still being studied and that research doctors are trying to find out more about it. As part of this research study, patients will be administered brentuximab vedotin in combination with a conventional re-induction chemotherapy regimen called MEC, which consists of the chemotherapy drugs mitoxantrone, etoposide, and cytarabine. Brentuximab vedotin has not been approved by the FDA for the patient's cancer. However, brentuximab targets a protein on tumors called CD30, and it is approved for other cancers which express CD30, and these include Hodgkin lymphoma. This means that the FDA has not approved giving brentuximab in conjunction with MEC for use in people, including people with this type of malignancy, acute myeloid leukemia (AML).

Mitoxantrone, etoposide and cytarabine are chemotherapy agents that are commonly used to treat individuals with relapsed AML. Brentuximab is an antibody-drug conjugate (ADC), which is the combination of an antibody (a protein that binds to cells) and a drug. Brentuximab vedotin works by using the antibody portion to enter into CD30-positive cells and then releasing the drug portion, which attempts to destroy the cell. Brentuximab vedotin has been used in laboratory and other research studies and information from those studies suggest that brentuximab vedotin may slow down the spread of cancers which express CD30. Some AML cell express CD30, so investigators hope that brentuximab vedotin will help with this type of AML.

The primary purpose of this research study is to determine the highest dose that Brentuximab vedotin can safely be given with MEC without severe or unmanageable side effects. The dose identified in this study will be used in future research studies.

If patients agree to participate in this research study they will be asked to undergo some screening tests or procedures to determine eligibility. Many of these tests and procedures are likely to be part of regular cancer care and may be done even if it turns out that patients do not take part in the research study. If patients have had some of these tests or procedures recently, they may or may not have to be repeated. These tests and procedures will include: a medical history, physical exam, performance status, pregnancy test, urine test, electrocardiogram, echocardiogram, blood tests, and bone marrow aspirate/biopsy. If these tests show that patients are eligible to participate in the research study, they will begin the study treatment. If patients do not meet the eligibility criteria, they will not be able to participate in this research study.

To start re-induction therapy, patients will receive brentuximab vedotin alone on Day 1. They will begin treatment with MEC (mitoxantrone, etoposide and cytarabine) a few days later (on Day 3). Since investigators are looking for the highest dose at which brentuximab vedotin can be safely administered with MEC without severe or unmanageable side effects in those with AML, not everyone who participates in this research study will receive the same dose of the study drug. The dose a patient receives will depend on the number of participants who have been enrolled in the study before that patient and how well they have tolerated their doses.

For this study, treatment will be broken up into segments. Study treatment will occur in two segments: 1) Re-Induction Therapy; and 2) Maintenance Therapy. Re-induction therapy, as described above, will be the combination of brentuximab vedotin followed on day 3 by MEC chemotherapy. The maintenance phase of therapy will only include brentuximab vedotin administered every 21 days for a total period of 12 months, and does not include any other chemotherapy. The treatment and assessments that may be required fo patients during these phases of therapy are explained below. The following assessments will be completed while patients are on the trial: physical exam, performance status, urine test, blood tests and bone marrow aspirate/biopsy.

The first part of the study treatment is called "re-induction". During re-induction, patients will be admitted to the Massachusetts General Hospital and will receive study treatment on an in-patient basis. Patients will receive brentuximab vedotin IV (intravenously or through a vein) alone on Day 1. They will then receive the following standard drugs (the MEC regimen) starting on day 3. This regimen includes the chemotherapy drugs mitoxantrone, etoposide, and cytarabine, all given by IV and beginning on Day 3 and continuing through Day 7.

If at the end of the re-induction course, the number of leukemia cells have not decreased as much as expected or desired, patients will be removed from the study and given alternative options.

The second part of study treatment is called "maintenance" and can be given on an outpatient basis in clinic. During maintenance, patients will be administered brentuximab vedotin once every 21 days, at the same dose as that given during the re-induction course. This 21 day period will be called a cycle, and will be repeated until 12 months have passed from the start of the maintenance therapy phase. During this phase, participants will not receive other chemotherapies and will not be hospitalized for treatment. During the maintenance phase, investigators will continue to collect approximately 2 to 3 teaspoons of blood for research purposes every 3-4 weeks.

Investigators would like to keep track of patients' medical condition and overall health following the 12 months of treatment on study. Investigators may ask patients questions about their general health, current medications and disease status. Investigators will also check on any new anticancer therapy patients may have started.

Inclusion Criteria:

• Pathologically confirmed, relapsed acute myelogenous leukemia following a remission duration of at least 3 months
• CD30 expressing AML
• Willing to use acceptable method of contraception

Exclusion Criteria:

• Have received systemic antineoplastic therapy, including radiotherapy within 14 days of study treatment
• Pregnant or breastfeeding
• Diagnosis of acute promyelocytic leukemia
• Refractory acute myeloid leukemia
• History of a different malignancy except if disease free for at least 5 years and at low risk of remission or one of the following within the past 5 years: cervical cancer in situ, basal cell or squamous cell carcinoma of the skin
• Equal to or greater than grade 2 ataxia, cranial or peripheral neuropathy
• Uncontrolled intercurrent illness
• HIV positive on combination antiretroviral therapy
• Diagnosis of active hepatitis B or C
• Current or history of congestive heart failure NYHA class 3 or 4
• Current or history of ventricular or life-threatening arrythmias or diagnosis of long-QT syndrome
• Systemic infection requiring IV antibiotic therapy within 7 days before first dose of study drug