Cell-type specific transcription is regulated by transcription factors. Transcription factors recognise their target genes through DNA binding domains, before using their transactivation domains to recruit the proteins necessary for transcription. This transactivation process remains poorly understood. Here, we couple Gal4-transactivation assays with comparative CRISPR-Cas9 screens, to identify the proteins required for transactivation by nine different transcription factors in human cells. Using this dataset, we can associate cofactors with transcription factors, classify transcriptional regulators as ubiquitous or specific, discover transcriptional co-dependencies and functionally dissect coactivator complexes. Specifically, we identify submodules within the Integrator and Mediator complexes, that function cooperatively, resulting in transcriptional co-dependencies between the subunits. More broadly, our screens demonstrate that transcription factors generally do not have dedicated, potent cofactors. Instead, they require a unique combination of cofactors that each contribute to transcription. We propose this diversity is essential for integrating complex information into the regulation of transcription.