According to the Memory Alpha wiki, it would be Geordia LaForge.
Geordi has held more ranks on screen than any other Star Trek character: he was an ensign in a flashback in TNG: "Identity Crisis", he was a lieutenant junior grade in TNG Season 1, a full lieutenant in TNG Season 2, a lieutenant commander in TNG Seasons 3 through 7 and the four Next Generation feature films, a commander in the illusory future of TNG: "Future Imperfect", and a captain in an alternate timeline in VOY: "Timeless".
That would be 6 ranks (Ensign, Lieutenant JG, Lieutenant, Lt. Commander, Commander and Captain), and includes all ranks with the exception of the flag ranks (Admiralty).