The presence of patient heterogeneity in dose finding studies is inherent (i.e. groups with different maximum tolerated doses). When this type of heterogeneity is not accounted for in the trial design, subjects may be exposed to toxic or suboptimal doses. Options to handle patient heterogeneity include conducting separate trials or splitting the trial into arms. However, cost and/or lack of resources may limit the feasibility of these options. If information is shared between the groups, then both of these options do not benefit from using the shared information. Extending current dose finding designs to handle patient heterogeneity maximizes the utility of existing methods within a single trial. We propose a modification to the time-to-event continual reassessment method to accommodate two groups using a two-parameter model and maximum likelihood estimation. The operating characteristics of the design are investigated through simulations under different scenarios including the scenario where one conducts two separate trials, one for each group, using the one-sample time-to-event continual reassessment method.