Right now it seems that he's just taking any opportunity to weaken everyone other than himself.
Littlefinger is intentionally setting the Boltons up or the Lannisters are indulging in wishful thinking by sending Jeyne north. From my experience of reading thirty some years of fantasy, I'd say that the Boltons are going down when Jon or Sansa exposes them... then again my experience told me that Ned would live, DOH!
Who do I think Baelish will ally himself with? GRRM paints him as the biggest opportunist in the Seven Kingdoms and mayhaps that is exactly what he is. But (and I've discussed this before) he might be a closet Targaryen supporter.
Baelish's grandfather was a merchant. His father's holdings amounted to a few acres of rocky island. How then did Petyr get to be fostered by one of the seven leading lords of the realm? It would have made more sense for a lesser lord of the Vale (any of them were still greater than the Baelishes) to foster Petyr than for Lord Tully of the Riverlands to take him in. For example, at the same time as Littlefinger was being fostered at Riverrun Ned and Robert were being fostered by Jon Arryn. Ned and Robert were both sons of one of the great seven lords and so both were fostered by another of the great lords. How did Littlefinger (as a son of the poorest noble family) get access to the same privileged education? My explanation is royal intervention.
I don't have any proof, but Targaryen blessings could have granted his grandfather nobility and secured his education. He might be fighting for their return.
If the Targs did not help his family, then the blessings came from the Arryns. If the Arryns did help the Baelishes, then Littlefinger only loves Littlefinger. He was not loyal to Jon Arryn, the man who gave him everything he had. Quite the opposite, he planned Jon's murder. He murdered his fellow conspirator Lysa, the woman who gave him everything she had.
He obviously wanted Jon dead. He wanted Robert dead. He wanted Eddard dead. He wanted Joffrey dead. He wanted Tywin dead (though he had no hand in it). He wants chaos around the throne. This helps him help either himself or the Targaryen's return.
In helping himself, he'll look for allies for a season. The Tyrells and the Arryns seem the most obvious alliances to me. But he could still remain allies with the Lannisters until they realize how he's betrayed them. The Martells and the Greyjoys might be possible alliances, but their goals seem to be at odds with his. He might find better success in the lesser family members... Arianne, Asha, Victarion, Theon, etc.
He seems hell bent on destroying the Tullys and the Starks. He's succeeded or at least they're being destroyed by his friends and allies.
He will not ally with Stannis because of Stannis unyielding nature.
I don't really think Littlefinger is a closet Targaryen supporter. Of course there's a chance because I'm not in control of the story. But I think, more and more, that Lord Petyr Baelish is for himself. I think he believes himself the smartest, cleverest, most daring, most patient, and ambitious man in the seven kingdoms. He does not believe in gods. He does not believe in nepotism. He believes in himself. His goal is the Iron Throne. For himself. He wants to be King Petyr I.
The Targaryens, Tullys, Starks and Lannisters would never stand for this, so they'll have to be eliminated. But some members of the Martells, Freys, Arryns, and Greyjoys will be more amenable to his ascension so they can be worked with.
Littlefinger's vision may be...
King - Petyr
Queen - Sansa, Margaery, Dany, Arianne, or even Asha (
though this marriage would be like that of Phillip II of Spain to Mary I of England, not only did they sleep in seperate beds... they lived in seperate countries)
Hand - Mace (a hollow title with no power whatsoever)
Lord of the Twins, Harrenhal and the Riverlands - Black Walder
Lord of the Vale - Nestor Royce
Master of Laws - Lyn Corbray
Lord of the Westerlands - Harry the heir (after marrying Myrcella)
Lord of the Northlands - Jorah Mormont or whoever marries Sansa
What about Bran? Sorry, Bran bores me. I don't give him any thought. Yes, he'll have some influence on the divine aspect of the story, but the political intrigue interests me much more.