

From what I can tell, their patterns are only on file during the transport, after which they are discarded. They imply it takes a lot of power and data storage to transport, meaning that they can’t just store everyone’s patterns.
There is an instance in beta canon, but just knowing that transporters and the title are related might spoil the entire plot. Thus, I am using nested spoilers so that people can check if it might be something they’re going to read without knowing exactly which thing it is.
Spoiler for IDW Trek comics
IDW Lower Decks comics/graphic novels spoiler
Warp Your Own Way Spoiler
Someone does overcome the power and storage problem and figures out how to make unlimited copies of a person, using this to repeatedly clone Captain Freeman and then Mariner to get secrets out of them. However, this was with years of research, and it was all destroyed within the comic plot to maintain continuity with the screen.
However, you could probably try replicating the two containment beams thing that happened to Riker and Boimler, though, duplicating Tuvix and splitting one.
Actually, they were stored across the entire station’s computer systems; only part of them was in Quark’s holosuite. It basically took every bit of storage on DS9 to store them.