  We argue that the consistent implementation of the multiple point principle
(MPP) in the general non-supersymmetric two Higgs doublet model (2HDM) can lead
to a set of approximate global custodial symmetries that ensure CP conservation
in the Higgs sector and the absence of flavour changing neutral currents (FCNC)
in the considered model. In particular the existence of a large set of
degenerate vacua at some high energy scale $\Lambda$ caused by the MPP can
result in approximate U(1) and Z(2) symmetries that suppress FCNC and
CP--violating interactions in the 2HDM. We explore the renormalisation group
(RG) flow of the Yukawa and Higgs couplings within the MPP inspired 2HDM with
approximate custodial symmetries and show that the solutions of the RG
equations are focused near quasi--fixed points at low energies if the MPP scale
scale $\Lambda$ is relatively high. We study the Higgs spectrum and couplings
near the quasi--fixed point at moderate values of $\tan\beta$ and compute a
theoretical upper bound on the lightest Higgs boson mass. If $\Lambda\gtrsim
10^{10} {GeV}$ the lightest CP--even Higgs boson is always lighter than $125
{GeV}$. When the MPP scale is low, the mass of the lightest Higgs particle can
reach $180-220 {GeV}$ while its coupling to the top quark can be significantly
larger than in the SM, resulting in the enhanced production of Higgs bosons at
the LHC.
