As long as vorticity quantization remains irrelevant for long-wave physics, superfluid turbulence supports a regime macroscopically identical to the Kolmogorov cascade of a normal liquid. At high enough wave numbers, the energy flux in wavelength space is carried by individual Kelvin-wave cascades on separate vortex lines. We analyze the transformation of the Kolmogorov cascade into the Kelvin-wave cascade, revealing a chain of three distinct intermediate cascades supported by local-induction motion of the vortex lines and distinguished by specific reconnection mechanisms. The most prominent qualitative feature predicted is unavoidable production of vortex rings of a characteristic size.