In drug development, early phase dose-finding clinical trials are carried out to identify an optimal dose to administer to patients in larger confirmatory clinical trials. Standard trial procedures do not optimize for participant benefit and do not consider participant heterogeneity, despite consequences to the health of participants and downstream impacts to under-represented population subgroups. Additionally, many newly investigated drugs do not obey modelling assumptions made in common dose-finding procedures. We present Safe Allocation for Exploration of Treatments (SAFE-T), a procedure for adaptive dose-finding that works well with small samples sizes and improves the utility for heterogeneous participants while adhering to safety constraints for treatment arm allocation. SAFE-T flexibly learns models for drug toxicity and efficacy without requiring strong prior assumptions and provides final recommendations for optimal dose by participant subgroup. We provide a preliminary evaluation of SAFE-T on a comprehensive set of realistic synthetic dose-finding scenarios, illustrating the improved performance of SAFE-T with respect to safety, utility, and dose recommendation accuracy across heterogeneous participants against a comparable baseline method.