In an embodiment, a processor includes a decode logic to receive and decode a first memory access instruction to store data in a cache memory with a replacement state indicator of a first level, and to send the decoded first memory access instruction to a control logic. In turn, the control logic is to store the data in a first way of a first set of the cache memory and to store the replacement state indicator of the first level in a metadata field of the first way responsive to the decoded first memory access instruction. Other embodiments are described and claimed.