Model-based optimization is an increasingly popular way of determining the values of the degrees of freedom in a process. The difficulty is that the available model is often inaccurate. Iterative set-point optimization, also known as modifier adaptation, overcomes this obstacle by incorporating process measurements into the optimization framework. We extend this technique to optimization problems where the model inputs do not correspond to the plant inputs. Using the example of an incineration plant, we argue that this occurs in practice when a complex process cannot be fully modeled and the missing part encompasses additional degrees of freedom. This paper shows that the modifier-adaptation scheme can be adapted accordingly. This extension makes modifier adaptation much more flexible and applicable, as a wider class of models can be used. The proposed method is illustrated through a simulated CSTR.