The 170 GHz 2 MW TE34,19-mode coaxial-cavity modular short-pulse pre-prototype gyrotron at KIT was recently modified in order to verify the multi-megawatt coaxial-cavity technology at longer pulses. In parallel, theoretical investigations on a possibility to operate the 170 GHz TE34,19-mode coaxial-cavity prototype at multiple frequencies up to 238 GHz have been started, with a goal to find a configuration at which the tube could operate in the KIT FULGOR gyrotron test facility using the new 10.5 T SC magnet. This paper indicates which adjustments have to be made and show the feasibility of the multi-frequency operation. Small modifications at the gyrotron cavity will support an RF output power of more than 2 MW at 170/204 GHz. Furthermore, a new gyrotron launcher has been designed capable of producing a Gaussian microwave beam with a Gaussian mode content of more than 96% at these frequencies.