A kitchen with cabinets mounted at staggered heights can create issues when using crown molding. This can happen when a shorter wall cabinet is next to a taller, diagonal wall cabinet. One solution is to make the shorter cabinet 12" in depth and the diagonal corner wall cabinet 15" deep. The 3" of extra depth provides a place for the crown molding to return into. If the cabinets are all 12" deep, you will have to use a piece of filler and return the crown molding back at a 22.5 degree angle to prevent issues with the door opening of the diagonal corner wall cabinet.
The picture below shows how to use a piece of filler to fill void between the crown molding and wall cabinet. Where the molding meets the block, the molding is cut at 45 degrees.
You will need to measure the height of the crown molding and cut a piece of filler to the same height and typically about 3-4" in length. You will then fasten the piece of filler to the top of the shorter wall cabinet and against the edge of the taller, diagonal wall cabinet. Cut the moldings with 22.5 degree miters and fasten to the filler.
When you raise the height of the wall cabinet above a microwave/hood in a run where all of the cabinets are 12" deep, the doors of that cabinet above the microwave/hood can be damaged by making contact with the crown molding next to it if the crown is returned back at a 90 degree angle. Returning the crown back at a 22.5 degree angle can prevent the doors from hitting the crown molding in a straight run.
There are some small things that you can do to improve the look of your crown molding. When you have a miter cut, use your touch-up marker to stain the inside edges of the crown before you fasten them together. When you have a long run that requires a joint, cut the angle so it faces away from the direction that you walk into a room. It makes the joint more difficult to see.