I largely think the game is in a pretty good place so I wouldn't likely change too much, and too much change wouldn't likely be possible within the existence of the game anyway.

1.) Rethink the removal of extra dungeons and instead expand the idea to potentially include the deep dungeon and exploration area content to allow for extra combat areas, including instanced areas, that had some additional challenge and rewarded more than just combat skill. It could be as simple as the return of Hard Mode dungeons or as complex as a completely new take on a randomly generated dungeon like space.
2.) Revamp the companion system to include everything from your Chocobo to Squadrons to Trusts. Leave main story NPCs as Trusts for specific instances but let you take your Chocobo into dungeons, let you take a Squadron member out into the world, etc. Just fold them all into one comprehensive system that works from level 15ish all the way through the game
3.) Add a Hall of the Novice and Hall of the Veteran to teach more advanced mechanical systems and role oriented tasks. Make completion of these a requirement at specified parts of the MSQ.
4.) Investigate what it would take to refresh the visual engine, the glamour system, the housing system, etc. Maybe these would never be able to be truly updated or revamped but lay out exactly what the challenges are and what the timelines are for giving them the fixes they deserve.