NVIDIA has an extension for corner-sampled images, which changes the rounding behavior (round-up instead of round-down) and minimum extents requirements (2 instead of 1) for image mipmaps.  Since this isn't a new format or supercompression scheme, it would require some other kind of metadata signaling.
I'm guessing this needs a vendor extension, otherwise there is no way to store a mipmapped KTX for this type of image unless it has PO2 dimensions and the mip chain ends at whatever dimension reaches extents 2 first.