Rapidly developing nanophotonics needs microresonators for different spectral ranges, formed by chip-compatible technologies. In addition, the tunable ones are much in demand. Here, we present site-controlled III-nitride monocrystal cup-cavities grown by molecular beam epitaxy. The cup-cavities can operate from ultraviolet to near-infrared, supporting quasi whispering gallery modes up to room temperature. Besides, their energies are identical in large 'ripened' crystals. In these cavities, the refractive index variation near an absorption edge causes the remarkable effect of mode switching, which is accompanied by the spatial redistribution of electric field intensity with concentration of light into a subwavelength volume. Our results shed light on the mode behavior in semiconductor cavities and open the way for single-growth-run manufacturing the devices comprising an active region and a cavity with tunable mode frequencies.