The ship whose command William Riker was offered in 2366, destroyed soon after at Wolf 359.
The USS Melbourne was a Starfleet starship of the 2360s. In 2366 command of the Melbourne was offered to William Riker, who once again had to weigh leaving the Enterprise-D for a ship of his own.
The Borg invasion intervened before Riker made his choice, and the Melbourne was among the ships destroyed by the Borg cube at Wolf 359. Its wreckage was seen among the debris of the battle, which also claimed Benjamin Sisko's ship, the USS Saratoga.