This paper presents the many-accelerator architecture, a design approach combining the scalability of homogeneous multi-core architectures and system-on-chip's high performance and power-efficient hardware accelerators. In preparation for systems containing tens or hundreds of accelerators, we characterize a diverse pool of accelerators and find each contains significant amounts of SRAM memory (up to 90% of their area). We take advantage of this discovery and introduce the accelerator store, a scalable architectural component to minimize accelerator area by sharing its memories between accelerators. We evaluate the accelerator store for two applications and find significant system area reductions (30%) in exchange for small overheads (2% performance, 0%--8% energy). The paper also identifies new research directions enabled by the accelerator store and the many-accelerator architecture.