Questions about thinking

"What do you believe about brand (or content, or design) that most agencies don't?" If they can't answer this, they don't have a point of view. You want to work with people who think about the work, not just execute it.

"Tell me about a project that didn't go as planned. What happened and what did you do?" This tells you more about the agency than any case study. How they handle difficulty is what you'll experience when your project gets difficult.

Questions about working style

"How do you handle disagreement with a client?" You want a studio that pushes back when they think you're wrong, not one that does whatever you say. The former produces better work. The latter produces expensive mistakes.

"Who is our day-to-day contact and how involved are the senior people?" Many agencies pitch with senior talent and deliver with juniors. Ask directly who is doing the work.

Questions about outcomes

"Can you show me work from this category? What did the client say it changed for their business?" Portfolio work is easy to curate. Client outcomes are harder to fake.

"What do your clients typically get wrong in the briefing process, and how do you help them avoid it?" A good agency has a clear point of view on this. It also tells you what they'll need from you to do their best work.