Additional backup to TimeMachine backup disk

Nope. Just plug it in. Time Machine will back it up. Just be sure the drive is not excluded in settings and that you have enough space available on the Time Machine drive.

I back up my Mac and an external drive to my Time Machine disk.

Just so I'm following. You want time Machine to back up your computer and an external drive (let's call it drive 2) to the Time Machine external drive (drive 1)? Certainly can do that. Just make sure that you have enough space and that the Drive 2 is not excluded from backup.

System Preferences > Time Machine > Options

Time machine will back up any disk connected to your computer so long as it is not excluded.