  We study various aspects of N=2 quiver-Chern-Simons theories, conjectured to
be dual to M2-branes at toric Calabi-Yau four-fold singularities, under
Higgsing. In particular we study in detail the orbifold C^4/Z_2^3, obtaining a
number of different quiver-Chern-Simons phases for this model, and all 18 toric
partial resolutions thereof. In the process we develop a general un-Higgsing
algorithm that allows one to construct quiver-Chern-Simons theories by blowing
up, thus obtaining a plethora of new models. In addition we explain how turning
on torsion G-flux non-trivially affects the supergravity dual of Higgsing,
showing that the supergravity and field theory analyses precisely match in an
example based on the Sasaki-Einstein manifold Y^(1,2)(CP^2).
