[3] When the block is in the Modified (M) state, neither a processor read (PrRd) nor a processor write (PrWr) request generates a snooped signal since the block already indicates that the most recent and correct value resides only in that cache.
At the same time, when it is in the modified (M) state, there is never going to be a bus write request (BusUpgr) from another processor as it does not have the cache block.
By the definition of the modified (M) state, only that processor has the block, rest all are invalidated and hence cannot initiate a BusUpgr request.
With a snooped write request (BusRdX), the block changes state to invalid (I) along with flushing (Flush) the data as another processor is writing to it, thereby losing its ownership on that block.
But in the case of MOSI protocol, where we have an additional state (owner), whenever another processor requests for a read operation, the block changes from modified to the owned (O) state and so retains the dirty block of cache, thereby removing the need to write back to the main memory immediately.
This deferral can save bus traffic and main memory writes in certain sequences of transactions.
MOSI therefore dispensed the initial memory write back and associated bus traffic which MSI would do.
MOSI focuses on reducing write backs and MESI attempts to reduce the number of bus transactions required after a read and write request from another processor.