At KIT, a modular 170 GHz, 2 MW TE34,19-mode coaxial-cavity gyrotron with advanced water cooling is ready for tests. The successful operation of this tube will be a first important step towards a possible future DEMO gyrotron. Nevertheless, looking forward, there are two questions to be answered: (i) what potential does the existing coaxial cavity offer with regards to MW-class multi-frequency operation also at higher frequencies, and (ii) what could be a different mode selection to achieve an even higher output power in a more compact gyrotron design. To provide an answer to (i), based on the 170 GHz, 2 MW preprototype the multi-frequency operation at multiples of the resonance frequency of the diamond disc RF output window was carried out. Additionally, a slightly modified cavity design was introduced. To answer the question (ii), the TE25,22-mode was chosen and compared with the results got for the TE34,19-mode. The extreme volume TE25,22-mode allows to reduce the beam radius by around 25 % and to increase the RF output power of the gyrotron by up to 30 %.