Transcription factors (TFs) regulate gene expression through complex and co-operative mechanisms. While many TFs act together, the logic underlying TFs binding and their interactions is not fully understood yet. Most current approaches for TF binding site prediction focus on individual TFs and binary classification tasks, without a full analysis of the possible interactions among various TFs. In this paper we investigate DNA TF binding site recognition as a multi-label classification problem, achieving reliable predictions for multiple TFs on DNA sequences retrieved in public repositories. Our deep learning models are based on Temporal Convolutional Networks (TCNs), which are able to predict multiple TF binding profiles, capturing correlations among TFs andtheir cooperative regulatory mechanisms. Our results suggest that multi-label learning leading to reliable predictive performances can reveal biologically meaningful motifs and co-binding patterns consistent with known TF interactions, while also suggesting novel relationships and cooperation among TFs.