I previously did an internship at Strategy&, so can share my experience (for the London office, at least).
First round interviews had two cases. The first was a "normal" candidate-led case. It also seems like interviewers have freedom to define their own cases, and they are not chosen centrally from a database (unlike at other firms like Bain or McKinsey)..
The second interview (and this might be specific to the London office) was a "pre-written case". All of the information in the case was presented in a pack of ~10 slides. The interviewer lets you read them alone for 10-20 minutes and he/she then comes back to discuss.Three broad questions were provided to guide the interview:
1) a market sizing/estimation question
2) a brainstorm question about a part of the case - e.g. how can company X increase revenue given issues they are facing?
3) Overall generic recommendation for the client?
Since I interviewed, I also heard that they added some team/group interviews as part of the process, but I am not familiar with these unfortunately.
I hope this helps!