Can I log multi-engine time abroad, when I'm not rated for multi in that country? I hold a multi-engine FAA CPL and want to fly a multi-engine aircraft in another country. The aircraft is not N-registered and I don't have a multi-engine rating in that country. Can I log the time in my FAA logbook? I'd like to log the hours under my FAA license.

More Details:
Country: Colombia (ICAO)
Role: Second in Command

The plane is a multi, I don't have multi license from the registration's country but I have FAA Multi license, so the idea is to fly it and log the hours using my FAA license can I do that ? Even if I don't have the license to fly that plane from the country of the registration ?
FAR 61.3 stipulates what is required to fly N-registered aircraft outside the united States.  There is nothing about flying non N-registered aircraft outside the U.S.  Rightfully so, the FAA does not have jurisdiction in that case.

To answer your question, you will need to reference that country's rule.  If they are an ICAO country, the rules are probably very similar.