Hmm... I posted this in another thread but it is still more of my ideal for DA4 than a simple Inquisitor as PC (and I admit to being an Inquisitor PC supporter). Thought it was an acceptable middle ground, though to pull it off it would require more of a DA2 style of storytelling. Sorry it is so long, but I had a lot of thoughts on how this could potentially work.
The game would revolve around two competing stories that slowly become more intertwined as the game progresses (in a sort of Halo 2 style). For the new PC the focus would be centered around the Social Unrest/Slave Rebellion arc. For the Inquisitor they are dealing with the pursuit of Solas (or looking for a way to deal with a borderline Demi-God) bringing them to Tevinter and getting help from Dorian. Early game (Chapter 1) the Inquisitor would mostly be out in the field (dungeon diving essentially) and the new PC would deal with City Exploration, allowing us to get to know both the country of Tevinter and it's Capital. You would switch between them only at key points during the main story and exploration would free and primarily uninhibited provided you didn't move past that plot point. Both character's get to deal with what they are intrinsically related to and wouldn't have to be forced into a conflicts that don't immediately concern them. Very little, if any direct interaction between the two characters would occur early on due to the different levels of Tevinter Society they would be working at, with each side having a more compact number of companions since the roster would be split between two groups.
The War with the Qunari would be a huge event and most certainly get both PC's dragged into it, assuming they are both in Tevinter. It would serve as an effective middle arc (Chapter 2) and be a great break from the main stories. Both characters would get to deal with their own problems in the War, perhaps meeting for the first time and ultimately this Arc would be the Catalyst for "Individual PC Stories" to start bleeding together. Getting a PC involved in the other's problems, whether they know it yet or not.
The Final "chapter" would be the conclusion of both of the "PC Stories" and both PC's (and their companions) would play a part in both finale's. Since Solas is a world altering event (and Tevinter reform is a Nation altering one) the confrontation with Solas would probably be the climax of the game, but perhaps the re-stabilization/reformation/enhancement of Tevinter is a required precursor to help in his defeat. This sort of storytelling would serve to keep both characters active and relevant, actually have them both retain combat and RPG game elements, and EVENTUALLY (and gradually) get them both involved in the matters that shouldn't have normally concerned them. Chapter 3 would also open up choosing between the two characters at will (outside of main story missions) to fully allow for the immersion in the game's RPG elements like exploration and gear grinding (think of it as the calm before the storm). This system would also effectively deal with the "romance" issues that comes from a DA4 that has a sole Inquisitor PC, but also gets rid of the negative side effects of the Inquisitor becoming merely an NPC (which if Hawke was any indication would be disastrous).
Of the Companions only Dorian, Solas & perhaps Sten should appear (who is now an Arishok now, go figure
) and none of them should be actual party companions. They should be left as NPCs. This will effectively deal with too much baggage being dragged in from previous games as Dorian and Sten's primary concerns are in the North (and always have been) and Solas doesn't care about Thedas in general.
Which leaves only one problem, how to deal with the problem of two PCs talking to each other? I thought of a simple (yet rough) way, though I'm sure there are better options out there (I just havn't thought of any atm).
At the beginning of DA4 you get to choose a default personality type for both PC's that takes over for the non active PC and allows them to communicate in a limited capacity (maybe not identical to what you would have chosen, but at least somewhat close) with your currently played PC in situations where the two are directly conversing. The default personality would only help to facilitate conversations, but would not force decisions for either character (at least not any major ones). If an important decision needs to be made by either character the players perspective shifts to that character. Direct contact would still need to be rather limited for this to work well and even if moving towards the same goal the PC's should be focused on different objectives (namely to reduce warping of the PC's RP legitimacy). Finally, if there is only one Big Bad then the player CHOOSES what PC is active for that conflict and subsequently for the conclusion of the game; while the other takes on their default personality and a somewhat more supportive role (though they could still have some good lines and should still be involved in the fight/ending). If there are two end targets they simply each go after a different one.