Is it Von Neumann architecture? Can you run code out of RAM? Because if so, you could totally run a real operating system that (I'm thinking of Fuzix, for example).
The CPUs architecture is Harvard, like in its prececessor. However, that seem to apply just to RAM, separated in the memory map in areas for instructions and data. For the ROM access, flash ROM accessed via SPI, looks like can be accessed from both data and instruction buses, so in that regard would behave like, de facto, von Neumann (?)
Anyway, for running a real OS you can use PIC32 microcontrollers: are full MIPS32, including memory protection, and there are many cheap implementations with 512KB of RAM and 2MB of ROM (even more). You can run e.g. LiteBSD on Olimex EMZ64 PIC32 board [1].