  The G++ content of the formulation of gravity and M-theories as very-extended
Kac-Moody invariant theories is further analysed. The different exotic phases
of all the G_B++ theories, which admit exact solutions describing intersecting
branes smeared in all directions but one, are derived. This is achieved by
analysing for all G++ the signatures which are related to the conventional one
(1,D-1) by `dualities' generated by the Weyl reflections.
