This pilot phase II trial studies how well high dose cyclophosphamide, tacrolimus, and mycophenolate mofetil work in preventing graft versus host disease in patients with hematological malignancies undergoing myeloablative or reduced intensity donor stem cell transplant. Sometimes the transplanted cells from a donor can make an immune response against the body's normal cells (called graft versus host disease). Giving high dose cyclophosphamide, tacrolimus, and mycophenolate mofetil after the transplant may stop this from happening.

PRIMARY OBJECTIVES:

I. To estimate the graft versus host disease (GVHD)-free relapse/progression-free survival (GRFS) at one-year post hematopoietic cell transplantation (HCT) and to evaluate the clinical activity of post-transplant high dose cyclophosphamide (PTCy).

SECONDARY OBJECTIVES:

I. To summarize toxicities/complications/infections including type, frequency, severity, attribution, time course and duration through 100 days post-transplant.

II. To estimate the cumulative incidence (CI) of acute and chronic GVHD. III. To characterize the time course of neutrophil and platelet recovery/engraftment.

IV. To estimate overall survival (OS), progression-free survival (PFS), CI of relapse/progression and non-relapse mortality (NRM) at 100 days, 1 year and 2 years.

V. To describe quality of life at 100 days, 6 months, 1 and 2 years. VI. To characterize immune cell reconstitution and T cell repertoire post high dose cyclophosphamide in mismatched donor HCT.

VII. To characterize quality of life.

OUTLINE:

CONDITIONING REGIMEN: Patients are assigned to 1 of 3 conditioning regimens at the discretion of the attending physician and principal investigator.

REGIMEN A (REDUCED INTENSITY CONDITIONING): Patients receive fludarabine phosphate intravenously (IV) over 60 minutes on days -7 to -3 and melphalan hydrochloride IV over 20 minutes on day -2.

REGIMEN B (MYELOABLATIVE CONDITIONING [MAC]): Patients receive fludarabine phosphate IV over 1-3 hours and busulfan IV over 3 hour on days -5 to -2.

REGIMEN C (MAC): Patients receive fludarabine phosphate IV over 60 minutes on days -7 to -5 and total body irradiation (TBI) twice daily (BID) on days -4 to -1.

TRANSPLANT: Patients undergo peripheral blood stem cell (PBSC) hematopoietic cell transplantation (HCT) on day 0.

GVHD PROPHYLAXIS: Patients receive cyclophosphamide IV over 1-2 hours on days 3-4, mycophenolate mofetil IV or orally (PO) thrice daily (TID) beginning on day 5 and stopping on day 35 if no severe GVHD is present, and tacrolimus IV continuously on days 5-180 with a taper beginning on day 90 in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up twice weekly for 100 days, twice monthly for 6 months, monthly until no evidence of GVHD, and then yearly for up to 2 years.

Inclusion Criteria:

• Patients with acute leukemia or chronic myelogenous leukemia with no circulating blasts and with less than 10% blasts in the bone marrow
• Patients with myelodysplastic syndrome (MDS) with intermediate-2 or high risk per International Prognostic Scoring System (IPSS) (or intermediate, high, very high risk by Revised International Prognostic Scoring System [IPSS-R]) or myeloproliferative neoplasm; primary or secondary if high-risk features or refractory disease
• Patients with chronic lymphocytic leukemia/small lymphocytic lymphoma, follicular, marginal zone, diffuse large B-cell, Hodgkin lymphoma, or mantle cell lymphoma with chemosensitive disease at time of transplantation; all types of lymphoma are eligible
• High risk, or refractory and relapsed multiple myeloma
• No available human leukocyte antigen (HLA)-matched related donor
• Available matched unrelated donor
• Ejection fraction at rest >= 50%
• Karnofsky performance status (KPS) >= 70
• Measured creatinine clearance more than 60 mL/min. The updated Schwartz formula should be used for pediatric patients (>=5 to 12 years old)
• Carbon monoxide diffusing capability test (DLCO) >= 50% (adjusted for hemoglobin) and forced expiratory volume in 1 second (FEV1) >= 50%
• Total bilirubin < 1.5 x the upper limit of normal; patients who have been diagnosed with Gilbert's disease are allowed to exceed the defined bilirubin value of 1.5 x the upper limit of normal
• Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) < 2.5 x the upper limit of normal
• Alkaline phosphatase < 2.5 x the upper limit of normal
• Female subjects (unless postmenopausal for at least 1 year before the screening visit, or surgically sterilized), agree to practice two (2) effective methods of contraception at the same time, or agree to completely abstain from heterosexual intercourse, from the time of signing of the informed consent through 12 months post-transplant
• Male subjects (even if surgically sterilized), of partners of women of childbearing potential must agree to one of the following: practice effective barrier contraception, or abstain from heterosexual intercourse from the time of signing the informed consent through 12 months post-transplant
• All subjects must have the ability to understand and the willingness to sign a written informed consent document

DONOR INCLUSION CRITERIA

• 7 out of 8 at high resolution using deoxyribonucleic acid (DNA)-based typing with either antigen or allele mismatched HLA (-A, -B, -C, and -DR) or 8/8 HLA-mismatched with either double DQ mismatch (10/12) or combined DQ and DP mismatch
• Donor must be willing to donate peripheral blood stem cells
• Suitable donor
• Medically cleared to donate per National Marrow Donor Program (NMDP)
• Absence of donor-specific antibodies (DSA) to the mismatched HLA-locus
• Donor choices per matched unrelated donor (MUD) committee according to center standard operating procedure (SOP)

Exclusion Criteria:

• Prior allogeneic transplant
• Active central nervous system (CNS) involvement by malignant cells
• Patients with uncontrolled bacterial, viral or fungal infections (currently taking medication and with progression or no clinical improvement) at time of enrollment
• Patients with transformed lymphoma (e.g., Richter's transformation arising in follicular lymphoma or chronic lymphocytic leukemia)
• Patients seropositive for the human immunodeficiency virus (HIV)
• Patients with active hepatitis B or C determined by polymerase chain reaction (PCR)
• Myocardial infarction within 6 months prior to enrollment or New York Heart Association (NYHA) class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities; prior to study entry, any electrocardiography (ECG) abnormality at screening must be documented by the investigator as not medically relevant
• Female patients who are lactating or pregnant
• Patients with a serious medical or psychiatric illness likely to interfere with participation in this clinical study
• History of another primary malignancy that has not been in remission for at least 3 years (the following are exempt from the 3-year limit: non-melanoma skin cancer, fully excised melanoma in situ [Stage 0], curatively treated localized prostate cancer, and cervical or breast carcinoma in situ on biopsy or a squamous intraepithelial lesion on PAP smear)
• Psychosocial issues: no appropriate caregivers identified, or non-compliant to medications
• Subjects, who in the opinion of the investigator, may not be able to comply with the safety monitoring requirements of the study