This trial aims to determine whether a combination transfusion of two kinds of donated but matched adult blood stem cells can have a beneficial effect on children with any one of 13 usually fatal solid tumours. The trial is being conducted at St Jude's Children's Hospital in Memphis. To be a participant in this study, the patient will have had to have a tumour that has not responded to treatment (refractory) or has relapsed. Each participant will also need a donor who is matched to them to avoid rejection of the donated cells (identical HLA haplotypes). The stem cells will be collected from the donor's blood following treatment with G-CSF. These stem cells will then be selected to produce two transfusions (one with cells expressing CD 3+ removed and one with cells expressing CD 45RA+ removed). Patients will then receive chemotherapy before receiving the stem cell transfusions on consecutive days. The safety and feasibility of this procedure will be accessed in terms of blood system recovery, infection rates and the one-year survival. The trial started in July 2012 and is expected to conclude in December 2015.