Coded caching is a communication method that exploits the data redundancy of receiver-side caches in broadcast-type communications, to achieve substantial throughput gains by delivering independent content to many users at a time. While though in theory the caching gains were expected to increase indefinitely, in practice the gains remained — under most realistic assumptions — hard-bounded by small constants, due to the fact that the underlying coded caching algorithms required the splitting of finite-length files into an exponential number of subpackets. We here reveal a new algorithm with which, by adding a single transmitter, we can double the finite-file-size receiver-side caching gains (and thus double the effective DoF). The work has direct extensions in MIMO-related coded caching, D2D coded caching and in distributed computing.