You would also require the instrument rating attached to your CPL(A)
Historically you would do the CPL(A) written exams, be issued with a CPL/IR
Prior to 1/7/1999 no MCC would be required and you would do the type rating for the multi crew ac. Confined to the RHS until you passed the ATPL ~ navigation block and had the appropriate flying experience.
Sitting the CPL exams are a thing of the past for the aspiring airline pilot. ATPL, now 14 exams the standard way.