Do you mean like you have yellow in the black? I think yellow and PK share a damper and when mine went one of the symptoms, before it completely drained the photo black, was that I had black in my yellow ink. It only happened on a few prints, and then I was out of ink.
My recommendation is to install QuadToneRip and print out a calibration page. It will print each color ink separately and should let you see if there's mixing going on. Just printing 0,0,0 may have the driver still using other inks, though I doubt much.
My 3880 has been converted to Piezography (after I fixed it). I have an old profile print on matte paper (hot press natural). The black patch is L*16.87436 a*1.129798 b*1.884137, but that's not ABW. I'll see if I can find one from the 3880 or I can print one from the 7900 when I switch it over to matte (same inks).