  Using SDSS DR15 to its full extent, we derived fundamental plane distances to
over 317 000 early-type galaxies up to a redshift of 0.4. In addition to
providing the largest sample of fundamental plane distances ever calculated, as
well as a well calibrated group catalogue covering the entire SDSS
spectroscopic footprint as far a redshift of 0.5, we present several
improvements reaching beyond the traditional definition of the fundamental
plane. In one approach, we adjusted the distances by removing systematic biases
and selection effects in redshift-magnitude space, thereby greatly improving
the quality of measurements. Alternatively, by expanding the traditional
fundamental plane by additional terms, we managed to remove systematic biases
caused by the selection of our SDSS spectroscopic galaxy sample as well as
notably reducing its scatter. We discuss the advantages and caveats of these
various methods and calibrations in detail. We found that improving the
fundamental plane distance estimates beyond the established methods requires a
delicate balancing act between various systematic biases and gains, but managed
to reduce the uncertainty of our distance measurements by about a factor of two
compared to the traditional fundamental plane.
