Hi there,
I'm going to be a bit of a contrarian here :)
I personally had case interviews with THREE companies (tier 2s) on one day. For my BCG interview, I flew to Boston quite sick (how times have changed...would never again), completed my interviews (2 case+fit rounds) and flew back home. As you see from my profile, I moved forward for all of them. I did not reschedule because it just looks so bad (for school recruiting).
Now, I'm not saying this is advisable. I was indeed tired. But, it's 100% do-able. And, this sort of thing is definitely expected once you're on the job anyway! (back to back workshops, land from a 4 hour flight and go straight to the client site for a 12 hour day, etc.).
So, think about you and your abilities. Reflect on whether you think you can do it or not....I gaurentee you've done worse (4 final exams at university in a day sort of thing). Adrenaline and coffee are powerful things :)
The reason I ask you to reflect, is, there is huge downside risk to trying to reschedule for school recruiting. They have a set day, and you need to stick to that day. They know if you're re-scheduling for another company and it's a bad look. I have heard of sutdents getting their interview invitation rescinded because of this. Note: This advice is for school-based recruiting NOT experienced/off-cycle recruiting (in which case rescheduling is fine).
(editiert)