Cassette compatability regarding Shimano 9 speed
The published max large cog for both RD-6700-SS and RD-6700-GS is 30. They can sometimes work acceptably with 32, but they're not designed to and it's hit or miss. The variance is because dropout design is not universal. Putting in a longer b-tension screw or running it in reverse can help. You can also get something like a Wolftooth Roadlink.

Total capacity is 34t for SS and 40t for GS.