I second most of the advice you already have below from other coaches. Some additional perspective based on my experience.
WHAT TO EXPECT
1) Less structure overall in case part → towards more of a discussion in which they hope to see a “respectful” peer who can keep up w/ their “mental CPU" pace, while having crisp communication and uber-structured and logical reasoning
2) More in depth FIT discussion: “website-type" answers on why firm x etc… and lack of serious maturity and self-introspection can really become a red flag here
3) “Curveballs” to test your “grace under fire”: I was asked tell me three reasons why we should not hire you :). Prepare to keep your composure and react logically and with confidence to whatever happens
4) Get to know a generally very smart and interesting top-1%-level professional. That at least was my experience - you do not get this opportunity very often in life, so remember to enjoy the process here
HOW TO PREPARE
1) Learn how to problem-solve in a very ambiguous context when you cannot revert to standard framework and you are by definition beyond your comfort zone
2) Double down on above-average verbal communication: prepare to be even more crisp, brief, refined + pay attention to the body communication
3) Focus on perfecting “nuances” beyond the fundamentals: to not leave “open flanks” (e.g. body language nuances, appearance, register of voice, ….). You do not need to be perfect but you do not have to expose weakness
4) Show maturity and deep self-reflection (e.g. on FIT): you need to be perceived as a mature senior professional regardless of your age and background, who has a very clear ideas on why he is taking this career choice
5) Learn to tolerate “curveballs” with grace: not losing composure and logical thinking despite very odd questions, reactions, is the name of the game here
6) Be thruthful to yourself: trying to sell a version of you that is very far from what you are will not fly. Those people are trained “people-decoder”: try to show your best true self (obviously controlling for red flags)
7) Have fun: seriously - we are the average of the 5 people we spend most time with. Getting the chance to speak w/ a Consulting Partner even if brifely, can, in my opinion, give you material to learn and move your “average” :)
Hope this helps.