The KIT 170 GHz TE34,19-mode coaxial-cavity gyrotron has been studied for an upgrade towards a dual-or even triple frequency operation at 170/204/(238) GHz. For this reason, the electron magnetron injection gun (MIG), the cavity and the launcher are simulated for operation with the TE40,23-mode and TE48,26-mode at 204 GHz and 238 GHz, respectively. A modification of the coaxial-cavity midsection length leads to an increase of the theoretical RF output power from 1.6 MW to around 2.1 MW at 204 GHz. Further, first experimental cold tests using a mode generator setup, show a successful excitation of the TE40,23-mode, which is the highest-order mode ever excited.