Ebuzz, a suggestion -
With some stiff paper make up three templates with pivot to spindle distance for common 9, 10, and 12" arms. As you swing an arc with each you will see where a second arm would be mounted behind the WT plinth. I imagine a 12" arm may work but am unsure about anything shorter.
If you determine that one or more options will fit and not have interference from the mounted WT arm, then proceed with mounting considerations. You could mount a second arm board off the back of your plinth, but that would require drilling somewhere along the back side. Your other option would be to mount the second arm on a weighted pod and position it (freestanding) behind your plinth for correct cartridge alignment.