Nero supports writing to multiple drives simultaneously. At least it does up to version 8 - I haven’t used any of the later versions. I used to use it regularly to write 3-4 copies of a CD simultaneously and it worked very well. (I think Padus Discjuggler also supported multiple drives, but that is going back a very long time and the company no longer exists.)
But that’s writing multiple copies of the same disc.
I’ve not encountered any problems running multiple instances of Nero 8 or CDBurnerXP. I haven’t tried writing from two instances simultaneously for some time (so my recollection may not be accurate), but I think worked successfully with Nero. (I haven’t tried it with CDBurner XP.)