When i was still with EMS/Rescue last year, there was a day where we had 5 responses. Started with a plane crash ( in a residential area), then 2 medical emergencies, a vehicular and another one that ended up with 13 px. A total of 29 px in a 24 hour duty.
For me personally, I have run 3 in a 24 hour period (storm watch, brush fire and medical). That same night the other truck in our station had two more (fallen tree on highway, possible transformer fire).
The department though, the 24 hour record is around 6 or 7. Surprisingly it was all fire except one IIRC.
7-10 I forget but they were all BS calls. The oil plant leaked the ordorant so everyone was calling. When I got home my house stunk to high heaven so I called the firehouse for a fan. Told them no lights not an emergency.........2 engines, lights, sirens and everyone laughing....