Well, once you get beyond "this arm and the other one" to eight or more arms (or more than three dimensions - but I digress) a multi-compartmental neural net is the way to go. As my biographer wrote about the Velantians:
No human or near-human mind can rally understand how the mind of Velantian works. A Tellurian can, by dint of training, learn to do two or more unrelated things simultaneously. But neither is done very well and both must be more or less routine in nature. To perform any original or difficult operation successfully he must concentrate on it, and he can concentrate upon only one thing at a time. A Velantian can and does, however, concentrate upon half-a-dozen totally unrelated things at once; and, with his multiplicity of arms, hands, and eyes, he can perform simultaneously an astonishing number of completely independent operations.
The Velantian's is, however, in no sense such a multiple personality as would exist if six or eight human heads were mounted upon one body. There is no joint tenancy about it. There is only one ego permeating all those pseudo-independent compartments: no contradictory orders are, or ordinarily can be, set along the bundled nerves of the spinal cord. While individual in thought and in the control of certain actions, the mind-compartments are basically, fundamentally , one mind.