  We consider supersymmetric models that include particles beyond the Minimal
Supersymmetric Standard Model (MSSM) with masses in the TeV range, and that
couple significantly to the MSSM Higgs sector. We perform a model-independent
analysis of the spectrum and couplings of the MSSM Higgs fields, based on an
effective theory of the MSSM degrees of freedom. The tree-level mass of the
lightest CP-even state can easily be above the LEP bound of 114 GeV, thus
allowing for a relatively light spectrum of superpartners, restricted only by
direct searches. The Higgs spectrum and couplings can be significantly modified
compared to the MSSM ones, often allowing for interesting new decay modes. We
also observe that the gluon fusion production cross section of the SM-like
Higgs can be enhanced with respect to both the Standard Model and the MSSM.
