This is specifically about technical interviews as one of several steps, though. "What is your plan for being effective in this job" is the kind of question that, in the OP's three-step interview, should be asked by the manager.

My current employer has candidates do a brief presentation about a project they are proud of. It's useful but imperfect (some people just aren't good at speaking to a group, which is okay for this job; some people aren't legally permitted to go into a lot of detail about their earlier projects).

Absolutely love that ! Weirdly it reminds me of ramit sethi briefcase "technique" which is roughly research the prospect, come up with some proposal that shows you can as value and pull it out of your briefcase at the opportune time.