There are two things that would prevent you from using all three communications protocols at the same time...
1. If there is a pin conflict. It would be worthwhile, regardless of your processor choice, to make sure that your uC has enough pins as to support all three protocols on separate pins without having to reconfigure the pins each time you want to use a different protocol. It would be impractical, from my experience, to try to use all three if they share pins, because this would mean having to perform low-level configurations each time you wanted to use a different protocol.
2. If you have a communications "module" that supports multiple protocols instead of the different individual peripherals. An example would the the USCI, or "Universal Serial Communications Interface", of the TI MSP430 family. This is a module that allows the user to configure it for either SPI, UART, or I2C. Having to use a single module and reconfigure it hundreds of times a second in order to communicate on all three protocols would be very difficult and incur a lot of overhead. That being said, if you had three of these USCI modules (just as an example), then you would be in the clear.
I hope this makes sense. I would consult the data sheets and make sure that you have the ability to pin out the various communications peripherals to separate pins, and that the communication suites are actually different protocols. I wish I could be more help, but unfortunately I can only offer advice, as I have never used any of Atmels chips.
Regards,
Willis