Hey buddy. So the file hierarchy is Project > Kits > Sounds
Your kits reside within your project.

You can use the C6 application on your computer to do a SYSEX dump (in your A4’s Global menu, arrow down to SYSEX, then SYSEX SEND) to select which kits you can save to your computer. Do this while in the project containing the kit or kits you want to move,

Then, open the new project and go back to the Global menu, and do a a SYSEX RECEIVE. Send the kits via C6.

Later this year an update to Overbridge will contain some librarian features, making this process much more streamlined.

Good luck!