Spend the extra money and take a private multi checkride before you get the commercial multi. You'll have the PIC mutli you'll need for the MEI. Also, do the commercial ratings and all three instructor ratings (if that's your desired course) as fast as your finances allow. The longer you wait in between ratings the longer you'll need to complete each one (and the greater the expense).

DPEs are running $200-400 right now. All that time after will be PIC. It's much more affordable than 13 or so hours of multi at $200-300 an hour later just trying to get to the requirements for the MEI.