The difficulty would be in the controlling of it with a quarry you can normally see where it is and then tell it where to go based on that with a tunnel bore it is normally quite far underground so you cant actually see it, it it is 4 directional you would need to basically have a cube of block breakers so the only place to teleport to to actually maintain or control it (seen as you kinda need to see where you are sending it) would be inside the cube then you cant get out easily without breaking it.
The actual build would be very simple and the same as a one directional tunnel bore just with at least four bore heads and four drives facing different directions.
Last season with my lets play I built a 6 directional tunnel bore. It consisted of "cars" 5 blocks cube, each car had a function, digging, power, control, movement, and a tunnel lining car that replaced the lining of the tunnel with a pattern of block so I could use it to make minecart tunnels. As there wasn't tube frames then I used a arcane bore to dig, but you could do the same thing with tunnel frames and block breakers. The trick I used for the frame motors was to make them two way by putting a deployer, filled with sonic screwdrivers, next to the frame motor responsible for actually moving the contraption with 2 other motors on each side for moving the motor back.
Here is the episode after I finished building it, I make a few tweaks and show off the tunnel it dug, shown in the preview image. The episodes before this are a tutorial on how to build and program it. I intend to build an improved version this season but not gotten to it yet.