The multiple point principle (MPP) is applied to the non--supersymmetric
two-Higgs doublet extension of the Standard Model (SM). The existence of a
large set of degenerate vacua at some high energy scale caused by the MPP
results in a few relations between Higgs self-coupling constants which can be
examined at future colliders. The numerical analysis reveals that these MPP
conditions constrain the mass of the SM--like Higgs boson to lie below 180 GeV
for a wide set of MPP scales Λ and tanβ.Comment: 26 pages, 3 figures, some minor changes to the tex