GAME OF THRONES: What is Littlefinger's Ultimate Plan?

(Spoilers ahead for Game of Thrones season 6.)

In the world of HBO's Game of Thrones, arguably the best player in "the great game" (as Tyrion refers to it in his conversation with Dany in the season 6 finale) is Petyr "Littlefinger" Baelish, the man who rose from nothing to become the Lord Protector of the Vale. Littlefinger has always been one of my favorite characters because he's constantly scheming, and he's almost always at least one step ahead of everyone else. He thrives on chaos, and excels at misdirection and pitting people against each other in service of his own agenda. But what is his ultimate plan? In last week's finale, he told Sansa that he wanted to sit on the Iron Throne with her at his side, and I thought that was it: his statement of purpose. But in an interview with Vulture, actor Aidan Gillen says — in typical Littlefinger fashion — there may be more to it than meets the eye.

Up until this point, he's been purposely vague about what he wants. But in the finale, he finally spells it out to Sansa, or so it seems. 
Sitting on the Iron Throne might be a bit on the nose. Maybe we should treat that with a degree of ...
A little bit of skepticism?
A little. I think I said it before — to you, actually — that sure, it's nice to be near the throne, to be able to counsel the person who sits upon the throne, but it's less interesting and more dangerous to be the one on the throne. He has said he wants that, he has said those words, but is that really what he means? I don't know.
Maybe it's just what he's telling Sansa to stir up her ambitions?
Yeah. It's unlikely, but not impossible. It's a real push. It's about pushing buttons in other people. You say what you want in order to have the maximum effect, and it's the more interesting proposition, of course — her being on the throne. It could help me retain her trust. He's not stupid, you know? He knows her trust is a very tenuous thing, post–Ramsay Bolton. But Sansa and Jon's relationship has just taken a more interesting turn, of course!

Gillen also spoke about that final mysterious look he shared with Sophie Turner's Sansa when Jon Snow was being crowned King in the North:

Speaking for Littlefinger, it was one of those moments where you go, "Fuck! Maybe this is a bigger thing than I thought it would be. How are we going to deal with this?" Given that he enjoys chaos and uncertainty and the thrill of all of that, it was a big moment for him.

Gillan is just the embodiment of this character on the TV show, and especially since his fate hasn't been revealed yet in the books, it's unlikely he knows what happens to Littlefinger beyond what we've seen so far. What do you think is Littlefinger's ultimate plan? Is it simply to rule, or does he have more complicated aspirations?

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