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Transcription factors (TFs) regulate gene expression by interacting with DNA in a sequence-specific manner. High-throughput in vitro technologies, such as protein-binding microarrays and HT-SELEX (high-throughput systematic evolution of ligands by exponential enrichment), have revealed the DNA-binding specificities of hundreds of TFs. However, they have limited ability to reliably identify lower-affinity DNA binding sites, which are increasingly recognized as important for precise spatiotemporal control of gene expression. Here, to address this limitation, we developed protein affinity to DNA by in vitro transcription and RNA sequencing (PADIT-seq), with which we comprehensively assayed the binding preferences of six TFs to all possible ten-base-pair DNA sequences, detecting hundreds of novel, lower-affinity binding sites. The expanded repertoire of lower-affinity binding sites revealed that nucleotides flanking high-affinity DNA binding sites create overlapping lower-affinity sites that together modulate TF genomic occupancy in vivo. We propose a model in which TF binding is not determined by individual binding sites, but rather by the sum of multiple, overlapping binding sites. The overlapping binding model explains how competition between paralogous TFs for shared high-affinity binding sites is determined by flanking nucleotides that create differential numbers of overlapping, lower-affinity binding sites. Critically, the model transforms our understanding of noncoding-variant effects, revealing how single nucleotide changes simultaneously alter multiple overlapping sites to additively influence gene expression and human traits, including diseases.