A JAA licence is not restricted to specific aeroplane categories - It is the same licence whether you fly a SEP, MEP or a B777. The aircraft on which you can exercise the privileges of your licence is determined by the separate aircraft rating(s) attached to it.
If you pass the CPL Skill Test on a SEP aeroplane, you will be issued with a CPL that includes a SEP Class Rating. To add a MEP Class Rating, you will need to complete an approved MEP Class Rating course (7 hours TK and 6 hours flight training, including 3.5 hours asymmetric) and pass the MEP Class Rating Skill Test.