I haven't visited these threads for nearly a year; please forgive me if someone else has shared a similar prediction in the meantime.

I predict that Quirrell's goal is to start a war between magical people and non-magical people.

The student armies have been taught combat skills, organization, and discipline but they have not been indoctrinated. The text does not show that the student armies have been guided toward one faction or another within Magical Britain. Quite the opposite, they have been taught to work together across the 'house' lines that may have divided them in the past.

It would be counter-productive to prepare tools that could be as easily used by your enemies as yourself. So we may reason that all members of the student armies are already on the side Quirrell wants them on. One thing all members of the student armies have in common is that they are members of Magical Britain.

I have found nothing to suggest international tensions, so a war against another magical nation would be out of place in the text, as I understand it.

On the other hand, Quirrell had a downright emotional reaction when Harry declared his aspiration to be a scientist in chapter 20. After the end, when we read through the story from the beginning, we will see that as the point where the villain's motivations are revealed: Quirrell wants to save the world from scientists and their careless exploration of powers they cannot contain.

Quirrell has been pushing Harry down a path of isolation. He created situations that built up Harry's distrust of authority. He cut Harry off from his friends. I believe he means for Harry to trigger the Great Muggle War by doing something grand and ill-advised that makes sense in the desperate state Quirrell intends to put him in.

My prediction of Quirrell's overall goal does not depend on my prediction of his intentions regarding Harry, and I am less certain of those. I feel there are pieces I am missing there.