The assessment of a structure’s performance is directly linked with reliability and safety issues, which are strongly associated to the random nature of load and resistance effects. Moreover, intrinsic properties of probabilistic models should relate to the commonly encountered dependencies among the input random variables. With respect to that, a significant advance towards effective modelling in current practice of structural reliability engineering has been achieved by integrating scalar indices, such as correlation coefficients. However, case may be that this approach overlooks, or even induces considerable uncertainties. Therefore, models which acknowledge and estimate this uncertainty type can serve the requirements for high modelling efficiency and improved predictions. In the present study, the uncertainties pertaining to multivariate idiosyncrasy are discussed, and a generalised dependence structure paradigm is suggested. The predictive potential of resulting models is demonstrated on showcase applications.