I think we can honestly say there won't be more parts to it - usually when an event has multiple parts that consecutively unlock (like the FFXIII Lightning event), they state as such on the Lodestone complete with a timetable of when to expect each part of the event. The Maiden's Rhapsody, however, has no such timetable or statement. Really,
Iroha's 'staying in Hydaelyn/Eorzea' at the end of the event
is merely a wry in-joke that this really is the end of FFXI's story and that the baton has been passed to FFXIV so to speak - and not a hint to expect further parts of that special event to unlock later.
Of course I may always be proven wrong though!