A novel interaction cavity has been designed for a gyro-oscillator, allowing co-harmonic generation at the 2(nd) and 4(th) harmonic resonances of the cyclotron frequency. The output aperture of the cavity has been designed to trap the lower harmonic, whilst allowing output of the upper harmonic. Results from recent numerical simulations, performed using MAGIC 3-D, are presented. The intended co-harmonic behaviour is observed, with simultaneous excitation of the 2(nd) and 4(th) harmonics. Refinement of the output structure is now being undertaken to ensure only the 4(th) harmonic signal is emitted