Just wrapped my Square PM loop last month. I'm a senior PM (7 YOE) and was interviewing for a Senior PM role on their seller products side. Sharing what I can.
The loop was 5 rounds: recruiter screen, hiring manager conversation, product design round, metrics / analytical round, and cross-functional stakeholder round. No case interview per se, but the product design and metrics rounds serve that purpose.
Product design round: They gave me a product problem in the Square ecosystem. Not going to give the exact prompt but it was merchant-facing, a real pain point real sellers have. The structure they expect: understand the user, define the problem space, prioritize, design a solution, think about success metrics. Don't skip the tradeoffs section. They pushed back when I proposed a feature: "what does this cost us? What does it do to our merchant support volume?"
Metrics / analytical round: This was heavier on data than I expected for a PM. They asked me to walk through how I'd set up an A/B test for a new checkout flow. Then: given these hypothetical results (they gave me a table), what would I conclude? Is this ready to ship? I also got asked how I'd detect if a new feature was causing unintended harm to a metric I wasn't tracking. Know your experimentation basics.
Hiring manager conversation: More behavioral than product. "Tell me about a time you shipped something you were proud of." "Tell me about a time you had to stop a project." "How do you work with eng leads who push back on your roadmap?" The manager was direct and had clearly read my resume.
Cross-functional round: Talked with a design lead and an eng lead. They wanted to see how I'd collaborate. I got asked "walk me through how you'd kick off a project with a new team you've never worked with."
Overall vibe: Square PM interviews are more rigorous than average, especially on the metrics side. They expect you to be comfortable with data. If your current PM role doesn't touch analytics much, study up on experiment design, conversion funnels, and how to define North Star metrics for a payments product.