How to extend Plackett-Burman design to further explore the interactions?

My situation is as follows: I have built a 2-level Plackett-Burman design with 10 factors (some are actual 0/1-variables, the others are numeric and I used the minimum and the maximum) and 32 experiments. The experiments are done, the results are at hand and the resulting (linear) models are ok but not quite satisfying.

So far those models only contain main effects and no interactions, because in the current design with 10 factors in 32 experiments the interactions are highly correlated und therefore using them in the models would not give meaningful results (right?).

The assumption now is that it’s probably the interactions, which are missing to make satisfying models, and to explore them I need to do more experiments. But what kind of design should I use here? My best guess so far is extending the 2-level design to a (face-centered) central composite design, because it’s said to be for "exploring non-linear effects". So is this the way to go or are there better methods?

edit: context is a plc controlled machine in which we are trying to detect whether or not the outcome of a production cycle (i.e. the product) will be satisfying or not. So the factors we are changing in the experiments are different machine settings and differences in the processed workpieces that influence the production process and the outcome.