Genomic data integration - the process of statistically combining diverse sources of information from functional genomics experiments to make large-scale predictions - is becoming increasingly prevalent. One might expect that this process should become increasingly powerful with the integration of more evidence. Here, we explore the limits of genomic data integration, assessing the degree to which predictive power increases with the addition of more features. We focus on a predictive context that has been extensively investigated and benchmarked in the past - the prediction of protein-protein interactions in yeast. We start by using a simple Naïve Bayes classifier for integrating diverse sources of genomic evidence, ranging from co-expression relationships to similar phylogenetic profiles. We expand the number of features considered for prediction to 16, significantly more than previous studies. Overall, we observe a small but measurable improvement in prediction performance over previous benchmarks based on four strong features. This allows us to identify new yeast interactions with high confidence, which we make available from networks.gersteinlab.org/intint/. It also allows us to quantitatively assess the inter-relations amongst different genomic features. It is known that subtle correlations and dependencies between features can potentially confound the strength of interaction predictions. We, thus, investigate this issue in detail through calculating mutual information. To our surprise, we find no appreciable statistical dependence between the many possible pairs of features. We further explore feature dependencies by comparing the performance of our simple Naïve Bayes classifier with a boosted version of the same classifier, which is fairly resistant to feature dependence. We find that boosting does not improve the performance, indicating that, at least for prediction purposes, our genomic features are essentially independent. We conclude that by integrating a few (i.e., four) good features, we approach the maximal predictive power of current genomic data integration; moreover, this limitation does not reflect (potentially removable) inter-relationships between the features.