Yes, this is possible, I have just created something like that.
Use the hardware SPI pins (10,11,12,13) to put the atmega328 in spi slave mode
I use software SPI on another set of pins to interface with an SD card and a Nokia 5110 display
For using arduino in slave mode I recommend reading
by Nick Gammon (thanks Nick, your code helped a lot). For using software SPI you can use shiftOut
http://arduino.cc/en/tutorial/ShiftOut
If you want to speed things up, look into fastDigitalWrite and fastDigitalRead, and how to build software SPI functions with it. You can find all code in the standard SD card library of the latest arduino build,
/libraries/SD/utility/Sd2Card.cpp
/libraries/SD/utility/Sd2PinMap.cpp
Cheers,
Jack