We have seen in Chapter 5 that the one-parameter CRM is consistent under certain model misspecifications, but is not generally so (Theorem 5.3). In order to avoid bias due to model misspecification, one may be compelled to consider a more realistic dose-toxicity function in the CRM than a one-parameter function. In this chapter we discuss the use of multiparameter models in the CRM literature. Section 12.2 first reviews dose finding methods based on nonparametric estimation, the so-called curve-free methods; and Section 12.3 presents the potential problems associated with these methods and provides remedies. Section 12.4 explores the use of two-parameter CRM and illustrates its pitfalls through numerical examples. Section 12.5 provides a literature review on the use of these multiparameter models in the CRM.