  We present the analysis of a very high-magnification ($A\sim 900$)
microlensing event KMT-2019-BLG-1953. A single-lens single-source (1L1S) model
appears to approximately delineate the observed light curve, but the residuals
from the model exhibit small but obvious deviations in the peak region. A
binary lens (2L1S) model with a mass ratio $q\sim 2\times 10^{-3}$ improves the
fits by $\Delta\chi^2=181.8$, indicating that the lens possesses a planetary
companion. From additional modeling by introducing an extra planetary lens
component (3L1S model) and an extra source companion (2L2S model), it is found
that the residuals from the 2L1S model further diminish, but claiming these
interpretations is difficult due to the weak signals with $\Delta\chi^2=16.0$
and $13.5$ for the 3L1S and 2L2L models, respectively. From a Bayesian
analysis, we estimate that the host of the planets has a mass of $M_{\rm
host}=0.31^{+0.37}_{-0.17}~M_\odot$ and that the planetary system is located at
a distance of $D_{\rm L}=7.04^{+1.10}_{-1.33}~{\rm kpc}$ toward the Galactic
center. The mass of the securely detected planet is $M_{\rm
p}=0.64^{+0.76}_{-0.35}~M_{\rm J}$. The signal of the potential second planet
could have been confirmed if the peak of the light curve had been more densely
observed by followup observations, and thus the event illustrates the need for
intensive followup observations for very high-magnification events even in the
current generation of high-cadence surveys.
