Multi - Scalar Models with a High Energy S & k *

_ ABSTRACT .w We study multi-Higgs models under the assumption that new physics exists at some high energy scale (RNP). If we perform the minimally required fine-tuning in order to set the electroweak scale (AEw), we find that the low-energy scalar spectrum is identical to that of the Standard Model with minimal Higgs content, up to corrections of order A$&/A&,. If, in addition, the model is supersymmetric down to a scale ASB << ANP, then the low-energy scalar spectrum is identical to that of the minimal supersymmetric extension of the Standard Model, up to corrections of order AiB/A&p. Additional light scalars, if they exist, would be a signature of additional low-energy symmetries. Flavor changing neutral currents and CP-violation effects due to Higgs exchange are also discussed. Finally, we clarify the Linde-Weinberg bound for the minimum Higgs mass in such models.