This is a multi-site study with plerixafor in pediatric cancer patients. The study will be conducted in 2 stages:

• Stage 1 is a dose-escalation study.
• Stage 2 is an open-label, randomized, comparative study using the appropriate dosing regimen identified in the Stage 1 dose-escalation study.

All participating patients will receive a standard mobilization regimen as per study site practice guidelines (either chemotherapy plus once daily granulocyte-colony stimulating factor (G-CSF) or once daily G-CSF alone). The only change to the standard mobilization regimen is the addition of plerixafor treatment prior to apheresis for all patients in Stage 1 (dose escalation), and for those patients randomized to the plerixafor plus standard mobilization treatment arm in Stage 2 (randomized, comparative).

Stage 1 will enroll at least 27 patients. Stage 2 will enroll at least 40 patients.

Inclusion Criteria:

• Age 2 to < 18 years during stage 1 and 1 to < 18 years during stage 2
• Ewing's sarcoma, soft tissue sarcoma, lymphoma, neuroblastoma, brain tumors or other malignancy (excluding any form of leukemia) requiring treatment with high dose chemotherapy and autologous transplant as rescue therapy
• Eligible for autologous transplantation
• Recovered from all acute significant toxic effects of prior chemotherapy
• Adequate performance status (for patients ≥16 years of age, defined as Karnofsky score >60 and for patients <16 years of age, defined as Lansky score >60)
• Absolute neutrophil count >0.75 × 10^9/L
• Platelet count >50 × 10^9/L
• Calculated creatinine clearance (using the Schwartz method): during study Stage 1, >80 mL/min/1.73m^2 and during study Stage 2, >60 mL/min/1.73m^2
• Aspartate aminotransferase(AST)/serum glutamic oxaloacetic transaminase(SGOT), alanine aminotransferase(ALT)/serum glutamic pyruvic transaminase (SGPT) and total bilirubin <3 × upper limit of normal
• The patient and/or their parent/legal guardian is willing and able to provide signed informed consent
• Patients who are sexually active must be willing to abstain from sexual intercourse or agree to use an approved form of contraception while receiving plerixafor and/or standard mobilization treatment and for at least 3 months following any plerixafor treatment

Exclusion Criteria:

• Any form of leukemia
• A co-morbid condition which, in the view of the Investigator, renders the patient at high-risk from treatment complications
• Previous stem cell transplantation
• Persistent high percentage marrow involvement prior to mobilization will be prohibited.
• On-going toxicities (excluding alopecia) Grade ≥2 resulting from prior chemotherapy
• Acute infection
• Fever (temperature >38.5°C) - if fever is between 37°C and 38.5°C, infection must be excluded as a cause
• Known HIV seropositivity, AIDS, hepatitis C or active hepatitis B infections
• Positive pregnancy test in post pubertal girls
• History of clinically significant cardiac abnormality or arrhythmia
• Use of an investigational drug which is not approved in any indication either in adults or pediatrics within 2 weeks prior to the first dose of G-CSF to be administered as part of the patient's planned standard mobilization regimen, and/or during the study up until engraftment of the transplant. If patients are on investigational drugs as part of their anti-cancer regimen, this should be discussed with the Sponsor before screening. Drugs approved for other indications that are being used in a manner considered standard of care for this transplant procedure are allowed
• The patient (and/or their parent/legal guardian), in the opinion of the Investigator, is unable to adhere to the requirements of the study