There has been many theories circulated.
I think that Solas is trying to help the People and has been for thousand of years. Every time he thinks he's done it and the People are finally okay, he goes back to sleep (uthenra) only to wake up later and find that everything he has done was for naught. He then has to start again. This is heavily hinted if you have high disaproval with him. He'll say something along the lines of "I've joined my fair share of causes in my time".
After the events of the temple of Mythal, he'll say something about never letting other people seize your power, lest they squander everything you have fought for.
He was revealed as Fen'Harel, the god of rebellion. If you read the codex entry for meaning of the word Harellan (trickster), it stems actually from "Noble struggle".
I don't think he has an endgame as catastrophic as expanding the veil (if so, what was the point of all of those damn Elven Artifacts).
There's also a banter between him and Dorian where Solas tells him "Hush Dorian. Empires rise and fall." hinting that restoring the glory or Arlathan might not be his goal either.
You'll also see in his conversations that he is against any form of slavery or control.
I think he simply wishes the People to be free and take back their place in the world. (They're currently either slaves in Tevinter, 2nd class citizens in Orlais and Ferelden or wanderers in the woods. Very far from what they were.)
Since his Orb was broken (if you're an elf, he'll say they were dedicated to specific members of the elven pantheon), I think he lost his "godhood" somewhat and thus needed to steal someone else's if he was to continue his fight for the People.
There's a lot more going on but I hope that answers your question.