Where I lived there were many home shows pushing new granite top specials. Many people bought a new granite top only to later realize just how ugly the old cabinets now looked. These people were now scared of disturbing and cracking their nice top if they bought new cabinets. This is where my trick comes in. I have done many successful kitchens this way. By the way I work with quality stock brand cabinets, no custom made.
Without ever disturbing the countertop, I break out the old base cabinet two at a time but always leaving support for the top. Since the top overhangs the top rail of the face frame, I cut a 1" cut from the bottom perimeter of the new base cabinet. Now it slides right under the countertop overhang. Then I prop it up with blocks and shims, screw it to the wall and add some liquid nails to where it touches under the CT. Once all the bases are installed I simply skin the exposed ends and the toe skin covers the toe kick face. Of course just R&R the uppers are put in the standard way. It is a lot of extra work on your knees but it pays the bills and no one else is doing it.
(Cabinet and Millwork Installation Forum)
From contributor M:
Iíve never done a whole kitchen but I have replaced cabinets that way. Just be very careful. One crack can cost you a lot of money!