This is what the EASA regulation says. In my opinion you would have to negotiate with the Authority to have them specify which extra training is necessary as in many countries they just don't have such experience yet. When I was trying to get the ansver from my country CAA, they were not able to give me more than this regulation.
Multi-crew pilot
2.5.2.1 Subject to compliance with the requirements specified in 1.2.5, 1.2.6, 1.2.7.1, 1.2.9 and 2.1, the privileges of the holder of a multi-crew pilot licence shall be:
a) to exercise all the privileges of the holder of a private pilot licence in the aeroplane category provided the requirements of paragraph 2.3.3 have been met;
b) to exercise the privileges of the instrument rating in a multi-crew operation; and
c) to act as co-pilot of an aeroplane required to be operated with a co-pilot.
(ICAO Annex 1)
FCL.405.A MPL Privileges
(a) The privileges of the holder of an MPL are to:
(1) act as co-pilot in an aeroplane required to be operated with a copilot; and
(2) exercise the privileges of the IR(A) in an aeroplane required to be operated with a co-pilot.
(b) The holder of an MPL may obtain the extra privileges of:
(1) the holder of a PPL(A), provided that the requirements for the PPL(A) specified in Subpart C are met;
(2) a CPL(A), provided that the requirements specified in FCL.325.A are met;
(3) the IR(A) in single pilot operations in aeroplanes provided that the licence holder has completed the training necessary to act as pilot-in-command in single pilot operations exercised solely by reference to instruments and passed the skill test of the IR(A) as a single pilot.
(EASA NPA 2008-17b)
FCL.325.A CPL(A) Specific
conditions for MPL holders
Before exercising the privileges of a CPL(A), the holder of an MPL shall have completed in aeroplanes:
(a) 70 hours flight time:
(1) as pilot-in-command;
or
(2) made up of at least 10 hours as pilot-in-command and the additional flight time as pilot-in-command under supervision (PICUS).
Of these 70 hours, 20 shall be of VFR cross country flight time as pilot-in-command, or cross country flight time made up of at least 10 hours as pilotincommand and 10 hours as PICUS. This shall include a VFR crosscountry flight of at least 540 km (300 NM) in the course of which full-stop landings at two different aerodromes shall be flown as pilot-in-command;
(b) the elements of the CPL(A) modular course as specified in paragraphs 11(a) and 12 of Appendix 3.D; and
(c) the CPL(A) skill test, in accordance with FCL.320.
(EASA NPA 2008-17b)