Ensuring profitable and sustainable cocoa bean yields under sub-optimal soil fertility conditions requires appropriate use of nutrient inputs. Currently, mineral fertilizers are not universally applied in cocoa and nutrient recommendations vary considerably from country to country, owing in part to a lack of knowledge on optimal fertilizer composition and rates. The collaborative research program CocoaSoils has established a network of eleven large reference trials across six countries, at locations representative of the world's main cocoa growing areas, with the aim of determining multivariate responses to varying levels of nitrogen (N), phosphorus (P), and potassium (K) throughout the different stages of cocoa development. A system for unified experimental design, implementation and data collection was created to maximise opportunities for cross-trial comparisons. An experimental design was developed that allows the estimation of joint N, P, K response surfaces under the assumption that single nutrient responses are constrained by co-limitation of the remaining nutrients. By assuming a specific nutrient response function, it is possible to estimate key parameters that can be used to calculate important measures such as maximum and minimum agronomic efficiency, available soil nutrients, economically optimal rates and water limited yields. Using computer simulations, we show that inference of multi-dimensional nutrient responses is possible, with estimations obtained for all parameters, albeit with considerable uncertainty. A first analysis of yield data from one of the trials demonstrated that the experimental design was successful in accounting for within-field heterogeneity but that effects of nutrient application are not observable at this early stage. We discuss the relevance of our results for improving Cocoa production. Keywords: Cocoa, Crop nutrition, nutrient response trial, statistics