Cell growth is determined by substrate availability and the cell's metabolic capacity to assimilate substrates into building blocks. Metabolic genes that determine growth rate may interact synergistically or antagonistically, and can accelerate or slow growth, depending on genetic background and environmental conditions. We evolved a diverse set of Escherichia coli single-gene deletion mutants with a spectrum of growth rates and identified mutations that generally increase growth rate. Despite the metabolic differences between parent strains, mutations that enhanced growth largely mapped to core transcription machinery, including the β and β' subunits of RNA polymerase (RNAP) and the transcription elongation factor, NusA. The structural segments of RNAP that determine enhanced growth have been previously implicated in antibiotic resistance and in the control of transcription elongation and pausing. We further developed a computational framework to characterize how the transcriptional changes that occur upon acquisition of these mutations affect growth rate across strains. Our experimental and computational results provide evidence for cases in which RNAP mutations shift the competitive balance between active transcription and gene silencing. This study demonstrates that mutations in specific regions of RNAP are a convergent adaptive solution that can enhance the growth rate of cells from distinct metabolic states.