It seems you are thinking about using the "Anchor" item as a bridge to link two separate sets of items from two separate MaxDiff studies. Market segmentation wouldn't work, as you've indicated.
I used a similar methodology to test the validity of the anchor item (dividing the items into two separate sets and trying to bridge them together using the anchor item...see a white paper at: https://www.sawtoothsoftware.com/download/techpap/dualresponsemaxdiff.pdf
I did this split-study design to test the validity of the anchor item, but I wouldn't recommend it as a way to bridge multiple groups of items together (divide and conquer) across respondents. Better idea would be to use "Sparse MaxDiff" or "Express MaxDiff" as described by Wirth/Wolfrath in their 2012 Sawtooth Software paper that may be downloaded from: www.sawtoothsoftware.com/download/techpap/2012Proceedings.pdf