1. A computer system for storing data to a system memory, the system comprising: the system memory; a cache comprising a cache directory having a plurality of directory entries; and a stepper engine, the stepper engine configured to perform a method comprising: initializing an internal congruence class register; accessing a plurality of directory entries of the cache directory in a current congruence class of the cache directory that corresponds to the internal congruence class register, the accessing of the plurality of directory entries being given a lower priority than other cache operations in the cache; determining that a specific directory entry of the plurality of directory entries in the cache directory has a change line state that indicates that the specific directory entry is modified; performing a store operation to send a copy of cache data associated with the specific directory entry to the system memory as part of a cache management function; updating the specific directory entry to indicate the change line state is unmodified; incrementing the internal congruence class register; and initiating an access to a next plurality of directory entries in a next congruence class of the cache directory based on the incremented internal congruence class register; the stepper engine further configured to perform the store operation to send the copy of the cache data associated with the specific directory entry to the system memory based on an ownership tag of the specific directory entry being set to an unowned state.