  We present an update to the EVEREST K2 pipeline that addresses various
limitations in the previous version and improves the photometric precision of
the de-trended light curves. We develop a fast regularization scheme for third
order pixel level decorrelation (PLD) and adapt the algorithm to include the
PLD vectors of neighboring stars to enhance the predictive power of the model
and minimize overfitting, particularly for faint stars. We also modify PLD to
work for saturated stars and improve its performance on extremely variable
stars. On average, EVEREST 2.0 light curves have 10-20% higher photometric
precision than those in the previous version, yielding the highest precision
light curves at all Kp magnitudes of any publicly available K2 catalog. For
most K2 campaigns, we recover the original Kepler precision to at least Kp =
14, and to at least Kp = 15 for campaigns 1, 5, and 6. We also de-trend all
short cadence targets observed by K2, obtaining even higher photometric
precision for these stars. All light curves for campaigns 0-8 are available
online in the EVEREST catalog, which will be continuously updated with future
campaigns. EVEREST 2.0 is open source and is coded in a general framework that
can be applied to other photometric surveys, including Kepler and the upcoming
TESS mission.
