SE specifically stated that you can't at the moment. See below for their stance.
Q. Will I be able to do the main scenario quests for the city-states other than the one I choose as my starting destination when creating a character? A. In fitting with the role of the adventurer as a champion of the nation in which his or her journey begins, players can partake only in the main scenario storyline of the starting destination chosen during character creation. We invite you to peruse the various plot synopses and NPC introductions to decide which epic adventure sounds most enticing to you!
Stories did not merge entirely in FFXI, each had a different conclusion.
Stories in FFXIV 100% merge. Sorry.
Stories were "100% merge" in FFXI when it released. Missions only went to Rank 5. Once you'd retrieved the Magicite, you were done. The later divergence after the defeat of the Shadow Lord was only put in later. So you can't say the quests won't diverge later on.