MapInfo has a new format called the MapInfo Extended format supported from MapInfo Professional version 15.2. The format enables a few new capabilities but most notably the ability to break the 2GB file size barrier and store multiple character sets in the same file:
http://web.pb.com/mapinfopro-oct-2015/MapInfo-Pro-v15.2-Breaking-Down-Barriers
It appears that the latest Beta of FME 2017.0 b17215 now includes a Reader for this new format, but this is a vote for a Writer for the same format please!

