There aren't really that many hands that push solid equity in a 4-way pot.  This hand is no exception.  At least if you assume that the other two players have somewhat reasonable hands.  Try running this hand against 30%+10%+10% to get an indication. (actual ranges are obviously somewhat different, but the end results won't differ all that much)

But more than the hand itself, stacks and position just don't seem great for a 4-bet here.  The most likely case is that you end up at least 3-way on the flop, and still probably at least a pot sized bet left with one of the players.  And out of position.  That's a perfect setup for making mistakes, and the 1-2% equity you *might* have pushed preflop doesn't make up for getting 200bb in bad or flipping on the flop imo.

I don't have pokerjuice someone else will need to run those numbers which will be more accurate.

Sure, if you have specific information about your opponents, then maybe you can make assumptions about their ranges.  I don't think you can automatically exclude AA from players ranges in general.  Certainly not from the 3-bettor, but given stack sizes, all players are not 4-betting all AA in this situation.

I had AKKx in my own 4-betting range for a long time, and it was basically just a disaster.  Half of the time I was pushing very little equity, and the other half I ran into AA and was completely crushed.

I can't give a definitive answer any better than you guys can come up with with calcs.  I just know from experience that people make a lot of mistakes jamming $ in with AKK in multiway pots because of the reasons Jonna mentioned (you don't push that much equity when none of them have AA, and you get stacks in awful when one of them does, AND you have some slight playability issues on flops).

It appears to me to be a very close spot.

Great question.

You're absolutely right that he is capped here, and we can definitely take advantage of that with parts of our range.

With KQJxss, my hand is just too good to turn into a bluff/semibluff.  I would choose to x/r turn with FDs that have no showdown value and my very weak Kx.  I could also choose some other weak hands if I think he'll be folding enough.  Double paired hands like 6644 make good semibluffs here since you almost always have 4 clean outs and you'll get paid off on the river by 9x (and 9x will rarely boat up on your boat cards).

His turn decision is a tricky one, and a bit too large to explore here.  I can say that it is theoretically fine to bet with a capped range in spots, but in this particular spot he doesn't have a lot to protect against AND I suspect he has few bluffs in his range (which need him to bet AA so that he can bet air), so checking back might make more sense.

I think how you play against unknowns is basically your strategy against the average player at these stakes. That does not mean GTO. Every decision someone makes is a commentary on their perception of the game balanced against their perception of their opponent. The fact that Phil is a thinking player, and not just clicking buttons (unless auto-piloting) means that we can infer what he thinks of the player pool at these stakes by his actions against unknowns.

I have a user-unfriendly macro that does the math for me based on the 3/4/5betsizes and effective stacks and MDFs if you want to PM me to get it. BEWARE though as it was more of an exercise to force myself to have to learn how the math worked rather than for it being that useful !!!

Say for sake of argument we limit our 4bet bet size to give villain pot odds between 2.25:1 and 3.25:1. I plug the numbers in and On this size our optimal value-hand contribution turns out to be between 51% - 56%, which gives us between 9 - 12 combinations of 4 bet bluffs with a value range of 12 {AA KK}.

We can even squeeze it up to (34.5 + 6.5)/6.5 : 1 or 6.3:1 for a min clickback 4bet, giving us up to 14 and a half combinations.