Basic way is to machine a rabbet in the back of the sides/top/bottom.

If the bases are 24" deep and the wall cabinets are 12" deep, it means that the upper portion of the corner bookcase on the 9:00 wall has to extend an extra foot to meet and form a corner at the 12:00 wall. We usually leave these corners of bookcases as dead. We don't extend them all the way to either wall.
I don't know if it's clear enough in this picture:

Casey

Blind corner or dead space.

Blind corners preserve shelf space at the inconvenience of not being able to see what is there.

Dead space is just that, closed off from access by the sides of the two book cases.

Casey,

Great pics. But I stil don't understand how to intersect a bookcase that has a 24" lower with a 12" (or so) upper with a bookcase that is ALL 12" (no 24" lower) from floor to ceiling. Maybe there isn't an elegant way to do it because after hours of searching online I haven't found one pic.

The room is almost square, 14' wide by 15' long. I want the 12" over 24" on the 14" wall and the regular bookcases on one side 15' wall

Well, the lower portion of the shallow run will end one foot before the upper portion, which will run until it hits the top section of the cabinets on the other wall. This would be detailed with the lower deep cabinet having a 12" blank surface for the lower bookcase to butt into. So, the base doors don't go all the way to the left corner, they stop a foot short and there's just blank plywood there.
Clear as mud?
Casey

I must be thick, I just can't picture it. I understand how the lower sections will intersect, I just can't figure out how the upper portions will. The upper portion of the bookcase section would effectively be sitting on the desk portion, right? I need a picture. If anyone happens to have one I'd appreciate you posting it.

I know I could just create a drywall box (or wood) in that corner, but I'd prefer another alternative if at all possible.

I'm not sure how it would look,On your top cabinets in the corner could you go 2 feet each way from corner then square out 12 inches to match other depth of top cabinets then diagional across.corner cab would be on angle to meet other
cabinets.....Clear as mud???

Not sure if this will clarify or confuse...

Thank you! Now I understand what it would look like. I guess I need to decide if I want the blind corner to be the way you drafted it, or have it be larger, extending the depth of the desk. But the picture really makes it clear for me. Thanks for the help everyone.