You have to open a crate to unlock gem extraction. I've done that with 2 characters. You probably can stack marked item copies from one character to another. But...
I have 2 items that have the gem extraction icon in front of them: 12 Crown Lethal Poison and 2 Crown Tri-Restoration Potion. But actually the first one is over 1200 pcs and the other over 400 pcs. It even says so if I mouse-over them in the top-right corner. I can't stack them in my inventory. I need 25 of each for a gem extraction. You would expect that I could have extracted 64 gems, but it sticks with the 12 and 2 pieces.
So, stacking only works for items you have split manually? It should automatically work for any copies you receive. Am I missing something here?