One of the most important questions in biology is how transcription factors (TFs) and cofactors control enhancer function and thus gene expression. Enhancer activation usually requires combinations of several TFs, indicating that TFs function synergistically and combinatorially. However, while TF binding has been extensively studied, little is known about how combinations of TFs and cofactors control enhancer function once they are bound. It is typically unclear which TFs participate in combinatorial enhancer activation, whether different TFs form functionally distinct groups, or if certain TFs might substitute for each other in defined enhancer contexts. Here we assess the potential regulatory contributions of TFs and cofactors to combinatorial enhancer control with enhancer complementation assays. We recruited GAL4-DNA-binding-domain fusions of 812 Drosophila TFs and cofactors to 24 enhancer contexts and measured enhancer activities by 82,752 luciferase assays in S2 cells. Most factors were functional in at least one context, yet their contributions differed between contexts and varied from repression to activation (up to 289-fold) for individual factors. Based on functional similarities across contexts, we define 15 groups of TFs that differ in developmental functions and protein sequence features. Similar TFs can substitute for each other, enabling enhancer re-engineering by exchanging TF motifs, and TF-cofactor pairs cooperate during enhancer control and interact physically. Overall, we show that activators and repressors can have diverse regulatory functions that typically depend on the enhancer context. The systematic functional characterization of TFs and cofactors should further our understanding of combinatorial enhancer control and gene regulation.