Chromatin, the nucleoprotein complex consisting of DNA and histone proteins, plays a crucial role in regulating gene expression by controlling access to DNA. Chromatin modifications are key players in this regulation, as they help to orchestrate DNA transcription, replication, and repair. These modifications recruit epigenetic 'reader' proteins, which mediate downstream events. Most modifications occur in distinctive combinations within a nucleosome, suggesting that epigenetic information can be encoded in combinatorial chromatin modifications. A detailed understanding of how multiple modifications cooperate in recruiting such proteins has, however, remained largely elusive. Here, we integrate nucleosome affinity purification data with high-throughput quantitative proteomics and hierarchical interaction modeling to estimate combinatorial effects of chromatin modifications on protein recruitment. This is facilitated by the computational workflow asteRIa which combines hierarchical interaction modeling, stability-based model selection, and replicate-consistency checks for a stable estimation of Robust Interactions among chromatin modifications. asteRIa identifies several epigenetic reader candidates responding to specific interactions between chromatin modifications. For the polycomb protein CBX8, we independently validate our results using genome-wide ChIP-Seq and bisulphite sequencing datasets. We provide the first quantitative framework for identifying cooperative effects of chromatin modifications on protein binding.