This study introduces a novel feature selection approach CMICOT, which is a further evolution of filter methods with sequential forward selection (SFS) whose scoring functions are based on conditional mutual information (MI). We state and study a novel saddle point (max-min) optimization problem to build a scoring function that is able to identify joint interactions between several features. This method fills the gap of MI-based SFS techniques with high-order dependencies. In this high-dimensional case, the estimation of MI has prohibitively high sample complexity. We mitigate this cost using a greedy approximation and binary representatives what makes our technique able to be effectively used. The superiority of our approach is demonstrated by comparison with recently proposed interaction-aware filters and several interaction-agnostic state-of-the-art ones on ten publicly available benchmark datasets.