Where in "/" should extra permanent disks be mounted?

According to the FHS link that you gave

 /mnt/  Temporarily mounted filesystems.

So I assume that you must mean permenantly mounted non-root non-system (meaning not /var/log or similar) filesystems.

I've always put them in /mnt/fsidentifier and then symlinked to then where needed.

So for instance, I had /mnt/website at one point, /mnt/appdata, /mnt/whatever, then symlink that. I never mounted anything directly to /mnt

If you wanted a "clean" solution, you could write a script to take the UUID of the filesystem, create a mount point for it (under /mnt or wherever you wanted), then mount the filesystem to the mountpoint.

Extra disks are typically mounted in a directory called /media/something where the something reflects the mounted device, e.g. /media/cdrom0 for the first CD-ROM device. This convention is widely followed under Linux for removable devices, and often but not always for permanent devices.

The FHS forbids distributions from using directories under /mnt because some administrators use /mnt itself as a mount point for temporary mounts. If you're the administrator, you can do what you like; just don't use /mnt itself as a mount point if you create directories under it.

Many places have their own convention. Some automounters have their own directory or directories (configured through /etc/fstab and /etc/auto.*); /amnt or /auto are typical names. Network mounts are often put under /net/$machine_name. Some places just use whatever went through the administrator's mind: /data, /local, /scratch, …

Of course, filesystems that have a specific place in the directory structure should be mounted there. For example, the mail partition is normally mounted directly on /var/mail or /var/spool/mail. If your home directories are spread between several disks, it's typical to mount them underneath /home, e.g. ~alice = /home/disk0/alice and ~bill = /home/disk1/bill and so on, if you want to expose the different disks in home directories. If you don't, then mount the home partitions wherever you like and create symbolic links or automounts in /home.

Wherever you like and where it makes the most sense for you. I have seen countless variants.

Myself, I usually mount them at /data0, /data1 or subdirectories below /data and put symlinks to the appropriate places (like /home).