If you are on one RTW the allowance for all the flights are the same. Since the RTW contains a trans atlantic you will have 2 pieces, 23 kg or 32 kg depending on the class you travel in.
As a star gold you will get one extra piece, so it is 3 x 23 kg or 3 x 32 kg.
As far as i know this is true for all star airlines - at least it was for me on the last trip in LH, LX, UA, SQ, Asiana and ANA