The haloscope is one of the most sensitive approaches to the QCD axion physics within the region where the axion is considered to be a dark matter candidate. Current experimental sensitivities, which rely on the lowest fundamental TM010 mode of a cylindrical cavity, are limited to relatively low mass regions. Exploiting higher-order resonant modes would be beneficial because it will enable us to extend the search range with no volume loss and higher quality factors. This approach has been discarded mainly because of the significant degradation of form factor, and difficulty with frequency tuning. Here we introduce a new tuning mechanism concept which both enhances the form factor and yields reasonable frequency tunability. A proof of concept demonstration proved that this design is feasible for high mass axion search experiments.