I was also wondering if it was possible to plug booth LCD touch screen and ethernet shields on my mega board.
After looking at pinouts, soldering some wires on the shield, I can confirm that it is possible.
It works perfectly (screen and network).
Didn't try the SD slots yet.
SD card works using the reader on the ethernet shield, not the one on the LCD shield.
I just plug the pin 4 on the ethernet shield to the pin 9 on the megaboard and change the code to use pin 9 as chip select.
const int chipSelect = 9;
If you are still interested, I can post schematic and pics.