  We investigate gravitational effects on the so-called multiple point
criticality principle (MPCP) at the Planck scale. The MPCP requires two
degenerate vacua, whose necessary conditions are expressed by vanishing Higgs
quartic coupling $\lambda(M_{\rm Pl})=0$ and vanishing its $\beta$ function
$\beta_\lambda(M_{\rm Pl})=0$. We discuss a case that a specific form of
gravitational corrections are assumed to contribute to $\beta$ functions of
coupling constants although it is accepted that gravitational corrections do
not alter the running of the standard model (SM) couplings. To satisfy the
above two boundary conditions at the Planck scale, we find that the top pole
mass and the Higgs mass should be $170.8\,{\rm GeV} \lesssim M_t\lesssim
171.7\,{\rm GeV}$ and $M_h=125.7\pm0.4\,{\rm GeV}$, respectively, as well as
include suitable magnitude of gravitational effects (a coefficient of
gravitational contribution as $|a_\lambda| > 2$). In this case, however, since
the Higgs quartic coupling $\lambda$ becomes negative below the Planck scale,
two vacua are not degenerate. We find that $M_h \gtrsim 131.5\,{\rm GeV}$ with
$M_t \gtrsim 174\,{\rm GeV}$ is required by the realization of the MPCP.
Therefore, the MPCP at the Planck scale cannot be realized in the SM and also
the SM with gravity since $M_h \gtrsim 131.5\,{\rm GeV}$ is experimentally
ruled out.
