Non-Fermi liquid (NFL) physics can be realized in quantum dot devices where competing interactions frustrate the exact screening of dot spin or charge degrees of freedom. We show that a standard nanodevice architecture, involving a dot coupled to both a quantum box and metallic leads, can host an exotic SO(5) symmetry Kondo effect, with entangled dot and box charge and spin. This NFL state is surprisingly robust to breaking channel and spin symmetry, but destabilized by particle-hole asymmetry. By tuning gate voltages, the SO(5) state evolves continuously to a spin and then "flavor"two-channel Kondo state. The expected experimental conductance signatures are highlighted.