There is a growing interest in early phase dose-finding clinical trials studying combinations of several treatments. While the majority of dose finding designs for such setting were proposed for oncology trials, the corresponding designs are also essential in other therapeutic areas. Furthermore, there is increased recognition of recommending the patient-specific doses/combinations, rather than a single target one that would be recommended to all patients in later phases regardless of their characteristics. In this paper, we propose a dose-finding design for a dual-agent combination trial motivated by an opiate detoxification trial. The distinguishing feature of the trial is that the (continuous) dose of one compound is defined externally by the clinicians and is individual for every patient. The objective of the trial is to define the dosing function that for each patient would recommend the optimal dosage of the second compound. Via a simulation study, we have found that the proposed design results in high accuracy of individual dose recommendation and is robust to the model misspecification and assumptions on the distribution of externally defined doses. © 2021 The Authors. Pharmaceutical Statistics published by John Wiley & Sons Ltd.