You can do this with the Flatpak version of Steam, but you have to give it access to the disks.

Flatseal is the easiest way to do this.

1. Open Flatseal
2. select Steam
3. scroll down to the "Filesystem" section
4. click on the + icon on the "Other files" area
5. either put in the full path, or use something like "/run/media" to give it access to all user-mounted storage devices (this value may vary depending on how the disk is mounted)

Restart Steam (if it was running). You should be able to access additional devices.