Understanding the mechanisms governing innovation is a central element of evolutionary theory. Novel traits usually arise through mutations in existing genes, but trade-offs between new and ancestral protein functions are pervasive and constrain the evolution of innovation. Classical models posit that evolutionary innovation circumvents the constraints imposed by trade-offs through genetic amplifications, which provide functional redundancy. Bacterial multicopy plasmids provide a paradigmatic example of genetic amplification, yet their role in evolutionary innovation remains largely unexplored. Here, we reconstructed the evolution of a new trait encoded in a multicopy plasmid using TEM-1 β-lactamase as a model system. Through a combination of theory and experimentation, we show that multicopy plasmids promote the coexistence of ancestral and novel traits for dozens of generations, allowing bacteria to escape the evolutionary constraints imposed by trade-offs. Our results suggest that multicopy plasmids are excellent platforms for evolutionary innovation, contributing to explain their extreme abundance in bacteria.