A sequentially adaptive Bayesian design is presented for a clinical trial of cord blood-derived natural killer cells to treat severe haematologic malignancies. Given six prognostic subgroups defined by disease type and severity, the goal is to optimize cell dose in each subgroup. The trial has five co-primary outcomes: the times to severe toxicity, cytokine release syndrome, disease progression or response and death. The design assumes a multivariate Weibull regression model, with marginals depending on dose, subgroup and patient frailties that induce association between the event times. Utilities of all possible combinations of the non-fatal outcomes over the first 100 days following cell infusion are elicited, with posterior mean utility used as a criterion to optimize the dose. For each subgroup, the design stops accrual to doses having an unacceptably high death rate and at the end of the trial selects the optimal safe dose. A simulation study is presented to validate the design's safety, ability to identify optimal doses and robustness, and to compare it with a simplified design that ignores patient heterogeneity.