  The derivation of the full Standard Model from noncommutative geometry has
been a promising sign for possible applications of the latter in High Energy
Physics. Many believe, however, that the Standard Model cannot be the final
answer. We translate several demands whose origin lies in physics to the
context of noncommutative geometry and use these to put constraints on the
fermionic content of models. We show that the Standard Model only satisfies
these demands provided it has a right-handed neutrino in each 'generation'.
Furthermore, we show that the demands can be met upon extending the SM with a
copy of the representation (1, 2, 1/2), but this has consequences for the
number of particle generations. We finally prove that the Minimal
Supersymmetric Standard Model is not among the models that satisfy our
constraints, but we pose a solution that is a slight extension of the MSSM.
