This paper explores c-optimal design problems for non-linear, multi-response models. A General Equivalence Theorem (GET) is provided and we discuss the influence from model and (co)variance parameters on the designs. Special focus is on a bivariate dose response model, one response being a primary efficacy variable and the other a primary safety variable. The aim is to construct designs that are optimal for estimating the dose that gives the best possible combination of effects and side-effects.