Bacterial transcription factors (TFs) with helix-turn-helix (HTH) DNA-binding domains have been widely explored to build orthogonal transcriptional regulation systems in mammalian cells. Here we capitalize on the modular structure of these proteins to build a framework for multi-input logic gates relying on serial combinations of inducible protein–protein interactions. We found that for some TFs, their HTH domain alone is sufficient for DNA binding. By fusing the HTH domain to TFs, we established dimerization dependent rather than DNA-binding-dependent activation. This enabled us to convert gene switches from OFF-type into more widely applicable ON-type systems and to create mammalian gene switches responsive to new inducers. By combining both OFF and ON modes of action, we built a compact, high-performance bandpass filter. Furthermore, we were able to show cytosolic and extracellular dimerization. Cascading up to five pairwise fusion proteins yielded robust multi-input AND logic gates. Combinations of different pairwise fusion proteins afforded a variety of 4-input 1-output AND and OR logic gate configurations.