This could be extremely spoilery, or it could be nonsense. Read at your own risk.
Petyr Baelish makes an unusual comment to Sweet Robin in this week's episode. I don't believe that to be an offhand comment about the fight at Winterfell. I think by "join the fray" he meant, “join the Frey.” A pun he alone understood. But I'm not sure it had such a straightforward meaning. I've heard some speculation on one of the podcasts I listen to (no idea which one) that he'd be joining the Freys in an attack on Winterfell to avenge Lady Walda Bolton, murdered by her enemy Ramsey.
There's a certain Elia Martell appeal to that as an idea, and it would certainly be interesting to see Petyr interact with Walder Frey. But what if I were to remind you of what they had in common? Petyr Baelish's backstory is rooted in his childhood friendship with his lifelong romantic interest, Caitlyn Tully. Though he was denied her hand in marriage after losing a duel to Brandon Stark (older brother to Ned), his affections for her and his inability to secure her due to being of lower station were important catalysts to the trajectory of his ambitions.
Now, let's remember why we hate Walder Frey so much. The Red Wedding. At the Red Wedding, Walder Frey arranges for the assassinations of Rob Stark, his pregnant wife, and Caitlyn Stark.
How you interpret this information depends a whole lot on how you think Petyr really felt about Caitlyn, particularly considering we did not see Petyr react to news of her death. Also, he very quickly transferred his affections to Caitlyn's daughter, Sansa, who I remember him commenting in the books was more beautiful than her mother. Even very early in the series, Petyr comments he's saving himself for someone who came from two very good bloodlines. I'm sure Caitlyn was highborn on both sides, but whose blood do we know about? I think it's been Sansa Baelish has wanted for himself since season 1.
I've heard Petyr Baelish called the Severus Snape of the Game of Thrones series, which is laughable in the extreme. Snape was the most loyal character in the whole of the Harry Potter series, completely devoted to a single largely unselfish cause. He could have gone on after the first wizarding war and lived a new life. He was a talented guy, he could have marketed those skills to do something other than what he hated, teaching school. Instead, he devoted himself to finishing what the one he loved started, protecting her son. He did this at great personal risk to himself. Petyr Baelish is the anti Snape. He does whatever will help him climb the ladder of chaos. He did have strong feelings about Caitlyn Stark, and he may well have loved her. But he has not, in the time since she died, truly served her interests. He lead on her sister and threw her through the moon door. He kissed her daughter, and then married her off to the worst person ever.
But- It's still hard to be sure with Petyr Baelish. He's a master manipulator, but he also has specific things he seems to want, and he does not react well to being denied.
Here's what I think: I don't believe Petyr Baelish has the least bit of interest in any true alliances with the Freys, unless such an arrangement were temporary. Eventually, I think Petyr Baelish will be responsible for the death of Walder Frey, and Frey will know that it's vengeance for Caitlyn's death.
What if Baelish helps organize the Northern Conspiracy to prove his loyalty to Sansa and the Stark brothers? What if he (with the help of Lord Manderly) bakes up a hearty Frey pie to serve to Lord Ramsey Bolton and Walder Frey, who may not even be aware his daughter is dead? What if Baelish is the one to inform Walder Frey of his daughter's death, and causes a Frey/Bolton altercation?
Frey pie for thought.