Thought I'd give it a go and see for myself what would happen if I pushed HP5-Plus to EI 12800. I have never pushed film before.
I shot one sheet at box speed (which I never do...usually EI 250), and another sheet at EI 12800. Developer was Ilfosol-3 1+9. 6.5 minutes for box speed negative, 18 minutes for EI 12800. (24C).
I scanned in both with no adjustments, then with the mid-tones overly lightened to show any degradation of blacks; then another example showing best possible image.
In the image there are two columns. Column on the left is box speed. Column on the right is EI 12800. Top row is scan with no adjustments in PS. Middle row shows extreme lightening of mid-tones to show degradation of blacks. Bottom row adjustments made for best image possible for both.
I would have to say I'm quite impressed. I can't see myself ever exposing film at such a high EI. Maybe 6400. Box speed gives pretty nice results.