Just finished my loop at Perplexity for a PM role. Didn't get the offer (they said the role was more technical than my background, which, fair), but I want to share what the behavioral portion looked like because it was different from what I expected.
First: they don't call it a behavioral round per se. It's more folded into the hiring manager conversation at the end of the onsite. But there were very clearly structured questions in there.
Questions I got (paraphrasing from memory): Tell me about a time you shipped something you weren't fully confident in. What happened. How do you decide what not to build? Give me a specific example. Tell me about a disagreement you had with an engineer. How did it get resolved. What's a product decision you made that turned out to be wrong? How'd you find out and what did you do.
All of these have a common thread: they want to see intellectual honesty. The "tell me about a product decision that was wrong" question is the clearest one. I've had interviewers elsewhere where that question was a trap (you give a small failure that was actually a win). At Perplexity the interviewer literally interrupted me when I started to spin it and said "what was actually bad about it."
They seem allergic to polish. A couple of my answers were a little scattered and they didn't seem to care. When I gave a tight, practiced-sounding answer it felt like the conversation cooled. When I gave a messy, honest one it got more engaged follow-up.
Values they implicitly telegraphed: bias toward action, comfort with uncertainty, being direct, caring deeply about the product's quality from a user POV. Made sense given what they build. If your instinct is to optimize for stakeholder management over product quality you'll probably not click.
Prep advice: know your actual failures and be specific. Don't over-polish your STAR stories for Perplexity. They can tell.