Getting an SIC type rating also seems, according to the FSDO, to NOT be possible if based on training/checking done by a foreign carrier or personnel. If the training program is not FAA approved and the checks, etc., are not done by FAA designees in FAA checked simulators, they wouldn't be valid for adding the SIC type rating to your US certificate, no matter HOW MANY signatures you get!
However, the FAA does have a special deal with Canada. If you have a Canadian license it's pretty easy to get the equivalent US license and ratings with only paperwork.