The evolution of protein-coding genes proceeds as mutations act on two main dimensions: regulation of transcription level and the coding sequence. The extent and impact of the connection between these two dimensions are largely unknown because they have generally been studied independently. By measuring the fitness effects of all possible mutations on a protein complex at various levels of promoter activity, we show that promoter activity at the optimal level for the wild-type protein masks the effects of both deleterious and beneficial coding mutations. Mutations that are deleterious at low activity but masked at optimal activity are slightly destabilizing for individual subunits and binding interfaces. Coding mutations that increase protein abundance are beneficial at low expression but could potentially incur a cost at high promoter activity. We thereby demonstrate that promoter activity in interaction with protein properties can dictate which coding mutations are beneficial, neutral, or deleterious.