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We consider the design of dose-finding trials for patients with malignancies when only a limited sample size is available. The small sample size may be necessary because (1) the modality of treatment is very expensive, and/or (2) the disease under investigation is rare, requiring a lengthy period to enroll a target patient population. Both of these are common in the field of adoptive immunotherapy, in which T cells are infused to prevent and treat infections and malignancies. The clinical trial described in this paper investigates a novel therapy to adoptively transfer genetically modified T cells in small pilot protocols enrolling patients with B-lineage malignancies. Due to the constraints of cost and infrastructure, the maximum sample size for this trial is fixed at 12 patients distributed among four doses of T cells. Given these limitations, an innovative statistical design has been developed to efficiently evaluate the safety, feasibility, persistence, and toxicity profiles of the trial doses. The proposed statistical design is specifically tailored for trials with small sample sizes in that it uses the toxicity outcomes from patients treated at different doses to make dose-finding decisions. Supplementary materials including an R function and a movie demo can be downloaded in the websites mentioned in the paper. [ABSTRACT FROM AUTHOR]