I did my CFII/MEI in the same day... be warned its a VERY long day. Total it was about a 12 hour day start to finish, about 8 hours of which is checkride (considering paperwork, debriefing each checkride, and a lunch somehwere in the middle). I did two separate orals and two seperate rides. Maybe your DPE would work both into one big checkride which would help... but if you fail something what would he fail, both CFII/MEI? This thought was why my DPE chose to do them separate.
I was very spent by the time the second practical came around and it was a boarderline pass due to my mental state and stress level of the day. Good luck to you if you do it, but if possible just do it 2 days back to back IMO. (I did both due to having to fly to the examiner, about 1.5 x2)