You might try a slightly different way:
- select your model
- click Tools --> Copy as new furniture
- right-click and Paste it in your existing model.
- check that this works; the copy should be exactly on top of the original.

- if that works, open your target file
- switch back to the source file, select the copy you made and do CTRL-C
- switch to the target file
- click in the top-right window to give it focus
- do CTRL-V to paste it there

If this doesn't work, let your father, mother, wife, boyfriend/girl, neighbour try it. If neither of them manages it, there's something strange going on. Goblins?