The Inquisition pretty much mows him down. In their eyes, the Evil Tevinter Magister's just killed the Herald of Andraste. Of course, they want revenge. Alexius dies, promising revenge from the Elder One and swearing to Felix he did it all for him. Not a minute later, the current ruler of Ferelden shoves the doors open and strides inside, demanding an explanation and kicking the mages out. The Inquisition — say, Leliana, who is here and is familiar with both Alistair and Anora (if less closely with the later), takes the mages as the allies; Cassandra would have conscripted them, but in the end, the result is much the same — the mages join the Inquisition.
Corypheus is pissed off. Obviously, he wanted those mages, was counting on having them, but with the Breach still hanging in the sky and the Herald of Andraste, that pest who ruined his plan, rumoured missing and presumed dead, he's not in such a hurry to attack Haven.
In the absence of the Herald, the advisors form a ruling council and lead the Inquisition jointly. They send teams on missions, and Cassandra, being an active combatant and often a team leader, is soon seen as the Inquisition's main representative. When the time comes to choose an Inquisitor, she is given the title without question (though it still surprises her. It is an honour she didn't expect.)
Not affiliated with the Venatori mages from all over Thedas pull together and find a way to close rifts. Even if they can't take on the Breach, at least, they repair the smaller tears. Solas helps, sending his agents to activate the artefacts to strengthen the Veil. Without the Herald and the anchor, he feels the responsibility for the Breach's existence all the more acutely. It doesn't make him come clean about his origin, but he does dedicate a lot of effort to righting the wrongs.
Despite all disadvantages, the Inquisition grows. People join not only to fight against the demons and oppose the Venatori and the red Templars, who crop up more and more with each passing day, but to avenge the Herald. It's on the lips of every soldier going into battle — "For the Herald! For the Inquisition! For Andraste!"
With the threat against Fereldans at an all-time high, the ruler mobilizes the army, and Josephine works out an agreement for them to send the troops to work with the Inquisition. The mages work with common soldiers well. It easies the fears.
In Tevinter, the news (and details) of Dorian's death reach Magister Pavus. Grieving and wreaked with regrets, he joins the opposition of the Venatori and drums up support for the Inquisition from that front. He works with Maevaris Tilani and her supporters in the Senate.
The Inquisition is invited to Halamshiral, and though they aren't able to save the Empress — perhaps, they were unaware of the plot, or perhaps, they knew but were unsuccessful, or perhaps, Leliana chose to let the Empress die. The reason why is unimportant. The end result, however, is Gaspard on the throne with Briala pulling the strings (They do have dirt on all of them, Leliana makes sure of that, but a war with Ferelden would benefit no one, and Leliana does sympathies with the elves).
This pisses Corypheus off enough to attack. Haven's left buried in snow, the refugees and soldiers all retreat through the Pilgrim's path while a chosen few stay behind to buy them time, but Cassandra sends the others off and meets Corypheus alone, much like the Herald would. She doesn't have the mark, but she is the Inquisitor and so the face of his opposition. The confrontation goes similarly, and much like the Inquisitor, she survives, the spirit of faith pressing from the other side of the Veil, whispering to her encouragements. She finds enough strength to stagger out of the mines. With a broken arm and cracked ribs, Cassandra walks.
Faith urges Cole to Cassandra's side. He finds her and helps her to the rest of the Inquisition's people. Exhausted and in pain, Cassandra masters up enough will to give a speech that rejuvenates the people. Morale is high. "It is a miracle!" is the prevailing exclamation. The faith in the Inquisitor and the Inquisition has never been so strong.
Solas discloses the location of Skyhold. In recent months, he has become an invaluable ally and a friend. Cassandra values his input greatly and doesn't question his knowledge too deeply. He saw it in the Fade, and as their expert on all things Fade-related, of course, that explanation is sufficient enough. They move in.
All around Thedas, more rifts crop up, and the teams of mages and Fereldan and Orlesian soldiers scramble to repair them. And then Corypheus subverts the Wardens. The skirmishes with the Venatori escalate into a war. It is a blow to all South.
Cassandra writes an angry missive to Weisshaupt, demanding that they deal with their own mess. She sends the letter before anyone can stop her (though only Josephine truly wanted to, and even she's fully behind the message). In answer, they deign to dispatch troops who join with the ever-growing Inquisition.
Around this time, a year passes. The world is not aflame, but war is raging. The Breach has been destabilizing for awhile, and Solas predicts it will tear open soon. The Inquisition's scouts monitor the situation, but so far nobody has come with a solution.
And into this mess, the Herald and Dorian return to the Redcliffe castle, now a major stronghold in the war. They are greeted like a miracle straight from the Maker.
AN. This is speculation, obviously, and just one way the story could have gone. As of now, I'm not planning to expand it, but if you like the idea and want to run with it, feel free to do so (just send me a link, please. ;)