After spending a countless amount of hours playing Persona 4 Arena, I can safely say that it's my favorite fighting game of all time. However, after recently getting the console version of BlazBlue: CSEX, there are many things from it that I would want to see added from it or adjusted in a sequel to P4A. Because of the Persona Team's focus on Persona 5 and Arc System Works' focus on BlazBlue: Chrono Phantasma as well as story implications, a P4A sequel is less than likely, but I would still like to list what I would want to see in one.
Special Character Intros
The video above shows special character intros in BlazBlue that I would love to see implemented in P4A2. People tend to skip fighting game intros after a while, but a lack of diversity does not help things and I think special intros add a lot to the presentation and to a game's overall style. The Persona 4 cast would be perfect for this and It's really disappointing to me that the only one of these in P4A is the Akihiko vs. Akihiko mirror matchup where they simply fist bump each other.
Matchup Specific Themes
Similar to wanting special character intros for specific matchups, I also want to hear themes for different matchups. This is something BlazBlue has plenty of and I love it. I wasn't that impressed by Persona 4 Arena's soundtrack (the lack of Shoji Meguro might be why), but Daisuke Ishiwatari does a good job of evoking specific feelings through his BB music and the character themes are a good indication of this as they fit their respective matchups so well. There are none of these in P4A outside of mirror matchups (with Reach Out to the Truth playing for P4 characters and Mass Destruction for P3 characters), but I think this is something that could be easily envisioned for the cast, just like special character intros.
A mode similar to Abyss
BlazBlue has this offline, single player mode by the name of "Abyss." The player chooses a level of depth they want to fight through (kinda like Tartarus!), selects their character and customizes them with items bought from the item shop that boosts their attack power, defense, speed or Heat gauge. Items bought from this shop can also have other special properties. Players then proceed to fight through "floors" of enemies with their own items, gaining in-game money in the process to buy better items in order to defeat even tougher enemies.
Because of the RPG nature of this mode, I think it's pretty clear why something like this would suit P4A.
Taunts + Special Character Dialogue
I don't know why P4A doesn't have these in the first place. And no, idle animations do not count because fighting games typically have those in addition to manually activated taunts.
Also, characters in these games talk a lot when fighting, but I think it's a nice touch when what they say changes depending on who they fight. P4A has some of this with Chie saying "Everything's great at your Junes!" during her auto-combo against Yosuke or Mitsuru yelling "Akihiko!" during her strong attacks, but I want more!
Online ranking system that doesn't suck
The PSR and Grade system that P4A currently uses is not only confusing, but also does not work well, especially since there are not that many people playing Ranked Matches these days. It's something that I'd want to see improved.
So that's all I could think of that I would really want in a sequel other than the easy stuff like more characters, backgrounds and more announcers.