jtw,
Thanks for the reply. In the meantime I have since solved this problem. If you want to Log a MAX31855 onto an SD Shield using an Arduino (which was my end goal) you cannot use the same clock, and MISO signals for both. That ended up being the cause of all the fuss. You must use an un-used digital pin for a mock clock and a mock MISO pin. The Adafruit MAX31855 library has you establish this in your sketch, its pretty self explanitory.
In my case I needed to read and log 4 seperate thermocouples. I ended up buying a Mega2560 for the extra pins and it works just great. Each slave (SD and thermocouple alike) has a chip select pin and the SD card shield uses the standard MOSI, MISO and SCK signals from the Arduino SPI interface. The only additional pins needed is like I said above a mock clock and a mock MISO pin that you set in your sketch for the Adafruit library.
I dont know if its possible to interface into the secondary SPI interface on the due yet. I have ordered a Mega prototyping shield and a kit of header pins to make a simple connector for both. I will update again when I get around to this.