I got a call from a friend who was really excited about an interview they had. They made it through the "important" rounds of the hiring process, with the direct team and hiring manager and were on to the cross functional leaders. She wanted to know how to handle interviewing with these heads of product and data science. This is the advice I had:
It's tricky. First understand the stage of the company. Generally speaking, the larger the company, the more structured the interviews. This company had a head of people and recruiter, but were still pretty small. That means the interviews will be structured, but with wiggle room.
For cross functional leaders, that wiggle room is your opportunity to shine. Left to their own devices, the cross functional leaders will focus the interview on what they think is important, which isn't always aligned with the hiring manager. Some of these folks pull a lot of weight internally and can in effect veto a hire. So while nailing the core interviews is important, you can't sleep on these.
What do you do? Filibuster. You need to take the reigns on the interview and drive it. First, find out who is interviewing you, if you don't know. The first step here is to get on the phone with the recruiter (I suggested cold calling the recruiter, but however you do it, get them on the phone asap).
An aside: The internal recruiter is your friend here. Rarely in the world do incentives align so well between parties, but in the case of the candidate and the internal recruiter your incentives are 100% aligned. That means you and them can work together to get you this job. Don't be afraid to reach out and get your questions answered.
In this case, you need to call the recruiter, get the names / bios of the interviewers at the least. In addition, questions like "How often have candidates failed at this step of the interview?" and "Do you know what interviewer X is looking for?" are gravy and can better hone your strategy.
You also want to discern how structured the interviews are. Occasionally, you will run into a cross functional leader that has a laundry list and they will adamantly stick to that list. It happens, it's good to know (from the recruiter) if that is what you are walking into. But in all of the other cases: Filibuster.
Filibustering, which is going on the offensive and asking questions about the functional leader's role, priorities and expectations for your role and organization, allows you to control the interview, avoid getting asked hard questions about their domain and overall demonstrate a consultative nature, which is almost always what a cross functional leader wants from their counter party.
You are auditioning for this job to these folks. They are expecting you to drive your domain. That means understanding their domain by asking thoughtful questions.
Once you know who you are talking to, think deeply about the role you are applying for, and craft the questions that you would need to do your job well. Ask those.
Toward the end of the interview, courteously end with 5-10 minutes left by saying "Thank you, this has helped my understanding a lot. Is there anything you wanted to ask me?" That demonstrates self awareness and will pre-empt post-interview feedback that the interviewer felt they didn't get what they wanted from the time.
Good luck out there!