Seems ok, I fold river vs unknown.

Agression on turn, river/ River bet would be useful.
I think I'm folding turn unless he has a higher turn bet vs misscb(or turn agg%) with a lowish river agg%. He should never bet worse for value OTT with this size 3way, also checking back his gutters are probably higher ev.
You draw very thin against his value range, and you will have QQ+, JJ, J9s, 98s, etc in this spot so it's not like this is the top of your range anyways.
I'd fold river too readless.

Very connected board multi-way, honestly a scary spot to bet flop. But out of everybody I think BTN has the least nutted range. Going to be a function of how tight a BTN CC range is compared to CORFI/ BB defend vs 2 people, and not having all 16 combo's of QT.
After CBing flop and 9x comes on turn, there will be a significant equity shift. Actually this would be a great spot for IP caller to bluff. His range will have many more 9x at this point and when he calls the multi way CB he drops a good amount of his air.
I like call turn call reasonable river bet on blank, if it isnt a reasonable bet I would fold. Also if I had 9K hands my decision on how to continue on turn/river; would come down to stats like river aggression, W$WSF, any reads, etc etc....
Thats why I would be C/Cing a significant portion of my range on the flop. Another advantage to that is BTN will play really straightforward. If he bets flop he will be pretty polarized to very strong TP, & strong-ish draws d in my opinion ( especially him being on the weaker side of a TAG). And since we are checking a significant portion of are range like this we will get to see what the other players do (fold/raise), and will be able to close action if we want.
If BTN raises and all other players fold, I would C/R aggressively, if there are callers I am going to most likely nit up and play a really tight range.
dddog