Having multiple victory conditions is for many L5R player a core feature of the game, so this should stay in some form or another. So, let's talk about it.
Military
Of course having a military victory condition is just fitting for a warrior culture that Rokugan is. But losing provinces was a vicious cycle for the player who lost them and thus always a problem in the game. Luckily I think that could be fixed by no longer destroying the pronces of the other players, but instead implementing territories that can be conqured in the middle of the table. This could be territories in the colonies, or the lands between the clans (the 4th Edition of the RPG, separated the clan lands stronger from each other, leaving my room between them over which the clans could fight). Or, in the Card Types thread Kyoden Kurosora also had the idea of the provinces not being used for card draw of dynasty cards, but as strongholds which grant special ponuses as long as they remain in play.
Political
The classic honour victory also always had its issues. First that it directly opposed the dishonour victory, and thus could lead to very long games, which is bad for a tournament envirnment, and was often not very fun for both sides. So, I think it should become a political victory condition. But of course playing honour and dishonour should still have a distinct feel to it, but in the end both could lead to political victories. Also, the abstract count to 40 should be probably replaced with a more objective oriented method, but if the objective that one has to achieve is laying as objective cards on the table, or are more like secret agendas one plays from the deck is something that has to be determined, but it could be different objectives for an honourable political victory and a dishonourable political victory.
Enlightenment
And the third of the victory conditions, also comes with its own baggage, how could it be any different. First, having the five rings in decks means the deck size is a factor, so with a possible change to maybe just one deck (instead of the two decks L5R had), it would mean it becomes harder to get the rings into the hand in teh first place and thus the requirement of cards that let you search for certain other cards increases (even more so then it already was). Such meta cards are often a problem in themselves, so maybe the objectives for enlightenment victory should not come out of a deck in the first place, but be open available in every game. Second the objectives themselves always have been an issue, AEG never got them balanced, and too often certain clans could not really even try to build an enlightenment deck, since they missed Shugenja, Monks, or Duelists. I think this has to change, the attunement to the five elements should be possible for everyone, so the five objectives should be possible with a wider variety of decks, but still challenging to pull off.
Other
The game has a history of additional vicory conditions from event cards. I think this should also be honoured, but is not needed to outright start with such tardition in the core game, but it should be kept in mind for later cycles.
So, anyone else with ideas regarding how the vicory conditions should be in the new game, or why it is important that certain things are kept like they have been?