Cyclophosphamide for Prevention of Graft-Versus-Host Disease After Allogeneic Peripheral Blood Stem Cell Transplantation in Patients With Hematological Malignancies

Inclusion Criteria: * Acute lymphocytic leukemia (ALL) in morphologic first complete remission (CR1) with high risk features defined as, but not limited to: evidence of adverse cytogenetics such as t(9;22), t(1;19), t(4;11), or mixed-lineage leukemia (MLL) rearrangements; presence of minimal residual disease; progenitor B-cell immunophenotype; high white blood cells (WBC) at diagnosis (\> 30,000/ul in B-ALL; \> 100,000/ul in T-ALL); or delayed attainment of CR (\> 4 weeks) after induction therapy; additional clinical characteristics deemed to confer a high relapse risk may be discussed with and approved by the Principal Investigator (PI) * Acute myeloid leukemia (AML) in CR1 EXCEPT patients with low-risk features defined as: * Inv 16 or t(8;21) in the absence of c-kit mutations * Normal karyotype who are FLT3-ITD-negative and NPM1-positive in the absence of c-kit mutations * Patients with respective "low-risk" features are eligible, however, if (i) more than 1 cycle of induction therapy was required to achieve CR1 (ii) the patient had a preceding myelodysplastic syndrome (MDS) other than myelofibrosis, or (iii) secondary AML * Acute leukemia in 2nd or greater CR (CR \>= 2) * Refractory or relapsed AML with =\< 10% bone marrow blasts and no circulating blasts or proven extramedullary disease * AML transformed from myelodysplastic syndrome (MDS) with \< 10% bone marrow blasts * MDS with following high risk features: * High risk cytogenetics (including, but not limited to: 7q--, inv\[3\], t\[3q\], del\[3q\] or complex karyotype) * International Prognostic Scoring System (IPSS) intermediate (INT)-2 or greater * Treatment-related MDS * Any phase of MDS if patient is \< 21 years of age * Chronic myelogenous leukemia (CML) beyond 1st chronic phase or resistant or intolerant to tyrosine kinase inhibitors (adults) or any phase (pediatric \< 21 years) * Chronic myelomonocytic leukemia * Philadelphia-negative myeloproliferative disorder * Lymphoma: relapsed chemotherapy-sensitive (complete or partial response) Hodgkin or non-Hodgkin lymphoma * Multiple myeloma-stage III * The patient or legal representative must be able to understand and give written informed consent * DONORS: The donor must be a genotypically HLA-identical sibling, a phenotypically HLA-matched first-degree relative, or an unrelated donor who is molecularly matched with the patient at HLA-A, B, C, DRB1 * DONORS: Donors must meet the selection criteria for administration of G-CSF (filgrastim) and apheresis defined by the Foundation for the Accreditation of Cell Therapy (FACT) and will be screened per the American Association of Blood Banks (AABB) * DONORS: Donors must be capable of giving informed consent Exclusion Criteria: * Prior autologous or allogeneic stem cell transplant * Performance status \> 2 (Eastern Cooperative Oncology Group \[ECOG\]) or \< 50 (Lansky; for patients \< 16 years old) * Uncontrolled infection; the protocol principal investigator (PI) will be final arbiter if there is uncertainty regarding whether a previous infection is under adequate control to allow enrollment in the study * Positive serology for human immunodeficiency virus (HIV)-1, 2 or human T cell lymphotropic virus (HTLV)-1, 2 * Left ventricular ejection fraction \< 45% or shortening fraction \< 25%; no uncontrolled arrhythmias or symptomatic cardiac disease * Symptomatic pulmonary disease; forced expiratory volume in one second (FEV1), forced vital capacity (FVC), diffusion capacity of the lung for carbon monoxide (DLCO) =\< 50% of predicted (corrected for hemoglobin); if pulmonary function tests cannot be performed, an oxygen saturation \< 92% on room air * Calculated (Cockcroft-Gault or appropriate calculation for pediatric patients) serum creatinine clearance =\< 60 mL/min; if the calculated CrCl is 50-60 mL/min, but a measured CrCl by 24 hour urine collection is \> 60 mL/min, this measurement is acceptable * Total serum bilirubin more than twice upper normal limit * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) more than 3-fold higher than laboratory upper normal limits * Female patient must have negative serum pregnancy test (all women of child bearing-potential must have test performed) * DONORS: Potential donors who for psychological, physiological, or medical reasons cannot tolerate administration of G-CSF or apheresis * DONORS: Donors who are allergic to filgrastim or Escherichia (E.) coli-derived proteins * DONORS: Donor-related risks to recipients * DONORS: Positive anti-donor lymphocytotoxic crossmatch * DONORS: Donors who are positive for HIV