RATIONALE: Giving chemotherapy before a donor umbilical cord blood stem cell transplant helps stop the growth of tumor cells. It also helps stop the patient's immune system from rejecting the donor's stem cells when they do not exactly match the patient's blood. The donated stem cells may replace the patient's immune cells and help destroy any remaining tumor cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and methylprednisolone after the transplant may stop this from happening.

PURPOSE: This phase I trial is studying the side effects of busulfan, melphalan, and antithymocyte globulin followed by umbilical cord blood transplant in treating young patients with refractory or relapsed malignant solid tumors.

OBJECTIVES:

• Examine the impact of the use of killer cell immunoglobulin-like receptor (KIR)-mismatched umbilical cord blood as a source of hematopoietic stem cells, after busulfan, melphalan, and anti-thymocyte globulin in pediatric patients with relapsed or refractory solid tumors.
• Determine the toxicity of this regimen, in terms of incidence of grade 3-4 acute graft-versus-host disease, donor/host chimerism, and cellular immunity against tumor cell lines, in these patients.

OUTLINE:

• Transplantation: Patients receive busulfan orally or IV every 6 hours on days -8 to -5, anti-thymocyte globulin IV over 6 hours on days -4 to -1, and melphalan IV over 15-20 minutes on days -4 to -2. Patients undergo allogeneic umbilical cord blood stem cell infusion on day 0. Patients receive sargramostim (GM-CSF) subcutaneously beginning on day 7 and continuing until blood counts recover.
• Graft-vs-host disease prophylaxis: Patients receive cyclosporine IV over 1 hour or orally twice daily on days -1 to 180 and methylprednisolone IV or orally once or twice daily on days 5 - 49.

Blood samples are collected periodically for immunophenotyping and flow cytometric analysis (including interferon gamma and other TH1 and TH2 cytokines).

After completion of study treatment, patients are followed periodically.

PROJECTED ACCRUAL: A total of 20 patients will be accrued for this study.

DISEASE CHARACTERISTICS:

• Diagnosis of malignant solid tumor

• Relapsed or refractory disease

  • No isolated local recurrence of disease (in the site of the primary tumor) > 1 year after completing therapy

• No brain tumors or brain metastases

• Unrelated cord blood donor available

  • May be HLA 6/6 matched (HLA-A, -B, -DR) OR mismatched for 1, 2, or 3 of these HLA loci, but must be mismatched for HLA-C group as indicated by their following killer cell immunoglobulin-like receptor (KIR) group specificity:

    • KIR2DL1

      • Cw 2
      • Cw 0307
      • Cw 4, 5, 6
      • Cw 0707, 0709
      • Cw 1204, 1205
      • All other Cw 15 alleles
      • Cw 1602
      • Cw 17
      • Cw 18

    • KIR2DL2

      • Cw 1
      • All other Cw 3 alleles
      • All other Cw 7 alleles
      • Cw 8
      • Cw 1202, 1203, 1206
      • Cw 1301
      • Cw 1402, 1403
      • Cw 1507
      • Cw 1601, 1604

• Cord blood specimen must have ≥ 1 x 10^7 nucleated cells/kg patient ideal body weight

PATIENT CHARACTERISTICS:

• ECOG performance status (PS) 0-2 OR Lansky PS 70-100%
• Cardiac ejection fraction ≥ 50%
• Creatinine clearance ≥ 50%
• Bilirubin ≤ 3.0 mg/dL
• DLCO ≥ 70% OR O_2 saturation ≥ 95% on room air

PRIOR CONCURRENT THERAPY:

• Prior autologous stem cell transplantation allowed