  Grand symmetry models in noncommutative geometry have been introduced to
explain how to generate minimally (i.e. without adding new fermions) an extra
scalar field beyond the standard model, which both stabilizes the electroweak
vacuum and makes the computation of the mass of the Higgs compatible with its
experimental value. In this paper, we use Connes-Moscovici twisted spectral
triples to cure a technical problem of the grand symmetry, that is the
appearance together with the extra scalar field of unbounded vectorial terms.
The twist makes these terms bounded and - thanks to a twisted version of the
first-order condition that we introduce here - also permits to understand the
breaking to the standard model as a dynamical process induced by the spectral
action. This is a spontaneous breaking from a pre-geometric Pati-Salam model to
the almost-commutative geometry of the standard model, with two Higgs-like
fields: scalar and vector.
