The universality assumption for the soft terms and some of its consequences are explained in section \[sec: universal\]. Section \[sec:mass\] contains the minimum conditions for the scalar potential as well as the scalar Higgs masses with the radiative corrections included in an approximation that is generally good, though we use the full expressions [@Elrc] in our numerical calculations. In section \[sec:stability\] we derive some approximate constraints from the stability of the vacuum to understand the pattern of the physical predictions. In section \[sec:inos\] we discuss some correlations in the mass spectrum along the same approximations. Then we summarize our implementation of the experimental and theoretical constraints on the model, in section \[sec:cuts\]. The main results of the careful scanning of the parameter space are displayed in the figures in section \[sec:spectrum\], with some emphasis on the sparticles more likely to be discovered at the colliders, with the exception of the Higgs sector that has been already presented [@ERS2]. The results are summarized in the last section. Some useful solutions of the RGE for the soft terms (with generic boundary conditions, for completeness) are listed in the Appendix.

1truecm

[General properties of the (M+1)SSM]{} {#sec:properties}
======================================

The superpotential of the (M+1)SSM 