The Gale correspondence provides a duality between sets of n general points in projective spaces and when equals . By a result of Mukai, the blow-up of at points say , can be realized as a moduli space of torsion-free rank semi-stable sheaves (with certain fixed Chern class datum) on the blow-up of in Gale dual points. In a recent work, Casagrande, Codogni and Fanelli use this to describe the Mori chamber decomposition of the effective cone of divisors of . It was shown by Castravet and Tevelev that the blow-up of at points for the case when and is no longer a Mori dream space. In joint work with Carolina Araujo, Ana-Maria Castravet and Diletta Martinelli we show that even in this case it is possible to give a Mori chamber type decomposition for a part of the effective cone.