I'm not a strong MP guy (as can be seen in a lot of my posts here) but if some things were added I would surely be more excited to try it out:
1: Character Creation
Let me customize my MP char just like I do for SP. It's one of the things that keep me coming back to the sp mode, creating my character makes me enjoy more playing as him/her. I tryed playing with the preset characters in DA:I's mp and I just became bored by them (I did wanted to play as Isabela though, but since her was locked until I reached the appropriate level, I simply quit). Quite the same happened with ME3 mp, but the gameplay was fun, so it kept me interested for some hours.
2: Let me do more than just shoot stuff
The main focus this time is exploration right? So bring this to the mp as well. Let us be the other pathfinders exploring other planets (and other parts of the planets the SP protagonist will explore).
3: Have it's own separate story, that happens in a parallel to the SP story.
It doesn't have to be something very well written, leave this to the SP. But just something happening to justify the action. No need to animated scenes here as well, just something like this:
And we can choose the answers in the dialogue weel as usual. That being said, make the stories happen in a parallel but never interact with each other. Keep the to experiences separated. Npcs can mention what's happening just to give the world consistency, but that's enough.
4: Last but not least, make the combat just as fun as it was in the ME3MP
No need to change anything here, just give us more things to do besides shooting and I'm in the boat ;P