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Cell therapies comprise one of the most important advances in oncology. One of the biggest challenges in the early development of cell therapies is to recommend safe and feasible doses to carry forward to middle development. The treatment involves extracting cells from a patient, expanding the cells and infusing the cells back into the patient. Each dose level being studied is defined by the number of cells infused into the trial participant. The manufacturing process may not generate enough cells for a given patient to receive their assigned dose level, making it infeasible to administer their intended dose. The primary design challenge is to efficiently use accumulated data from participants treated away from their assigned dose to efficiently allocate future trial participants and recommend a feasible maximum tolerated dose (FMTD) at the study conclusion. Currently, there are few available options for designing and implementing Phase I trials of cell therapies that can incorporate a dose feasibility endpoint. Moreover, the application of these designs is limited to a traditional dose-finding framework, where the dose-limiting toxicity (DLT) endpoint is observed in early cycles of therapy. This paper presents a novel phase I trial design for adoptive cell therapy that simultaneously accounts for dose feasibility and late-onset toxicities. We apply our design to a phase I dose-escalation trial of Rituximab-based bispecific activated T-cells combined with a fixed dose of Nivolumab. Our simulation results demonstrate that our proposed method can reduce trial duration without significantly hindering trial accuracy. [ABSTRACT FROM AUTHOR]