Most of your ideas would serve to diminish rather than expand the function of a breadboard.
*Access points for multimeter (on the back of the board perhaps, or along the side?)
With .1 spacing, what would you use? A post sticking up? A BARE METAL post? Don't you think it would be easy to short to adjacent rows? I think it would be a better solution to create a test lead for that.
*Crocodile clip access points (along the sides of the board)
Again, Alligator clips are big, plus you confine any usable pins for it to particular rows, which doesn't work well in the real world.
*Modular assembly of multiple boards (in 3 dimensions!)
They make small, medium, and large, and even multiples of each mounted on the same backing board, along with banana lugs. 3D might sound cool, but how are you going to check connections on the lower board?
*Something for cable management (hahaha)
Not a whole lot you can do other than use the correct length wires and be neat about laying it out on the board
*Maybe some guiding lines for intuitive understanding of the conducting strips within the breadboard for newbies
Don't really think that is necessary. Most power rails already are marked, and even indicated if not continuous. Rows are rows, columns don't matter.
*Designated I/O pins
For what particular thing? What if I don't use that particular thing? My I/O pins are different than yours. You cannot make a one-size-fits all in this respect. With an open breadboard, any uC I/O can be wired to the breadboard as easily as the next, and without limiting what has to go where
*In-built power lines
Done already. Combination banana screw lugs.
*Mountable on a variety of micro-controllers (especially the Arduino of course)
Most uC's that are small enough to put on a breadboard already ARE breadboard friendly. The few that are not have adapter boards in order to do this if that's what you want. An Uno or Mega isn't breadboard friendly because there wouldn't be much breadboard left, but that has been addressed too. Just mount the Uno in between a couple breadboards
I'm not saying to NOT try, but I'm saying you better be VERY clever about it. Maybe it would be better to make a test lead adapter board, where you could properly space out test points/posts with a elevated ground bar for attaching all the neg alligator leads. It would attach to the breadboard with standard wiring. You could even put another mini usb connector for when you need a second 5v supply.