In another word - 'No, you don't', not in the UK at least. However, the rules in Italy may be different.
JAR-FCL1 requires MCC training before the addition of the first multi-pilot aeroplane type rating. The CJ1 is not certified as a multi-pilot aeroplane, no matter how it may be operated. What's more, FODCOM 5/00 states: "Pilots operating SPA under JAR-OPS rules, i.e. as multi-pilot, will not be required to undergo further Multi-Crew Co-operation (MCC) training for endorsement of a Multi-pilot aeroplane (MPA) on their licence provided they have operated multi-pilot for an AOC operator for a minimum of 500 hours and have undergone two (OPCs).", so get a 525 on your licence, operate it for 500hrs multi-pilot and you then avoid the need for a MCC course at all.