An operation combiner receives a series of commands with read addresses, a modification operation, and write addresses. In some cases, the commands have serial dependencies that limit the rate at which they can be processed. The operation combiner compares the addresses for compatibility, transforms the operations to break serial dependencies, and combines multiple source commands into a smaller number of aggregate commands that can be executed much faster than the source commands. Some embodiments of the operation combiner receive a first command including one or more first read addresses and a first write address. The operation combiner compares the first read addresses and the first write address to one or more second read addresses and a second write address of a second command stored in a buffer. The operation combiner selectively combines the first and second commands to form an aggregate command based on the comparison.