I would experiment with capturing a noise print in Audition and using the noise reduction process, then see if I could manually clean up a little bit more from that manually. With background dialog, this may not work, depending on the clip, though.
My second trip around I would try simply keyframing gaps in the primary dialog to reduce the presence of the background.
Without hearing the clips, these are only guesses as to how to approach it. The more presence the background dialog has, the more of a challenge this will be.
I am sure others will chime in with some great (and better) ideas as well.
System:
Dell Precision T7600 (x2)
Win 7 64-bit
32GB RAM
Adobe CC 2015.02 (as of 6/2016)
256GB SSD system drive
4 internal media drives RAID 5
Typically cutting short form from HD MP4 and P2 MXF.