  Determining which small exoplanets have stony-iron compositions is necessary
for quantifying the occurrence of such planets and for understanding the
physics of planet formation. Kepler-10 hosts the stony-iron world Kepler-10b
(K10b), and also contains what has been reported to be the largest solid
silicate-ice planet, Kepler-10c (K10c). Using 220 radial velocities (RVs),
including 72 precise RVs from Keck-HIRES of which 20 are new from 2014-2015,
and 17 quarters of Kepler photometry, we obtain the most complete picture of
the Kepler-10 system to date. We find that K10b (Rp=1.47 Re) has mass
3.72$\pm$0.42 Me and density 6.46$\pm$0.73 g/cc. Modeling the interior of K10b
as an iron core overlaid with a silicate mantle, we find that the iron core
constitutes 0.17$\pm$0.11 of the planet mass. For K10c (Rp=2.35 Re) we measure
Mp=13.98$\pm$1.79 Me and $\rho$=5.94$\pm$0.76 g/cc, significantly lower than
the mass computed in Dumusque et al. (2014, 17.2$\pm$1.9 Me). Internal
compositional modeling reveals that at least $10\%$ of the radius of Kepler-10c
is a volatile envelope composed of hydrogen-helium ($0.2\%$ of the mass, $16\%$
of the radius) or super-ionic water ($28\%$ of the mass, $29\%$ of the radius).
Analysis of only HIRES data yields a higher mass for K10b and a lower mass for
K10c than does analysis of the HARPS-N data alone, with the mass estimates for
K10c formally inconsistent by 3$\sigma$. Splitting the RVs from each instrument
leads to inconsistent measurements for the mass of planet c in each data set.
This suggests that time-correlated noise is present and that the uncertainties
in the planet masses (especially K10c) exceed our formal estimates. Transit
timing variations (TTVs) of K10c indicate the likely presence of a third planet
in the system, KOI-72.X. The TTVs and RVs are consistent with KOI-72.X having
an orbital period of 24, 71, or 101 days, and a mass from 1-7 Me.
