Does a multi-engine rating propagate down from commercial to private?
Note Part 61.31(c):


  (c) Aircraft category, class, and type ratings: Limitations on the
  carriage of persons, or operating for compensation or hire. Unless a
  person holds a category, class, and type rating (if a class and type
  rating is required) that applies to the aircraft, that person may not
  act as pilot in command of an aircraft that is carrying another
  person, or is operated for compensation or hire. That person also may
  not act as pilot in command of that aircraft for compensation or hire.


Since you will have the Category and Class rating, then you may carry another person.

Your old license says:

Private Pilot
Airplane Single-engine Land
Instrument Airplane


Your new license will say:

Commercial Pilot  
Airplane Multi-engine Land  
Instrument Airplane   

Private Privileges  
Airplane Single-engine Land  


You may fly under part 91 ASEL, AMEL, and IFR

You may fly part 119 or 135 (or other commercial operations) AMEL and IFR1. You may NOT fly part 119 or 135 or any commercial operations ASEL. If you want to fly ASEL in a commercial operation, you will need to upgrade your ASEL by passing another commercial checkride in an ASEL.

This is the back of my certificate. I took the ASES checkride when I had a Private certificate.



1. Assuming you have the correct medical and any other checkouts you may need