Interestingly, SPI does seem to work fine on the Mega in test cases.
While MOSI, MISO, and SCK are on pins 11, 12, and 13 respectively on the Uno, those change to 51, 50, and 52 on the Mega. I initially daisy chained two LTC2400 analog-to-digital modules onto the SPI bus, just like I had them on the Uno, but immediately ran into issues. In theory these devices should handle SPI in the same manner, just with different pins. While working on a new revision of a project, I moved from an Arduino Uno to an Arduino Mega.