I've got a student about to finish up his Private MEL and Instrument ratings.
He decided to do both in the Duchess, so he'll take both checkrides at once since the DPE agreed.
When he successfully completes both checkrides (as I understand it, one flight/oral but two 8710s), his certificate will say:
PRIVATE PILOT
AIRPLANE SINGLE AND MULTIENGINE LAND
INSTRUMENT AIRPLANE
No further limitations to CLT or VFR only. If he doinks part of the "multi ride" like doing the Vmc demo or engine failures, etc. he won't even get to the "instrument part" of the ride such as approaches and holds. However, if he completes that and does not successfully complete the instrument portion he will be limited to VFR only for Single and Multiengine airplanes.
Only one instrument rating, the kicker is the SE approach in the twin. According to the DPE that did my CMEL, that's why they limit you to VFR only for twins if you don't do the approaches. Doing a two (or three, four, eight, fifty, etc.) engine approach is like doing an approach in a single except at higher (usually) speeds and more levers to play with...with the SE approach you've got the assymetrical thrust thing to deal with.
-mini