  We explore further our recent generalization of the $\mathcal{N}=4$
superconformal Chern-Simons theories of Gaiotto and Witten. We find and
construct explicitly theories of enhanced $\mathcal{N}=5$ or 6 supersymmetry,
especially $\mathcal{N}=5$, $Sp(2M)\times O(N)$ and $\mathcal{N}=6$,
$Sp(2M)\times O(2)$ theories. The $U(M)\times U(N)$ theory coincides with the
$\mathcal{N}=6$ theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We
argue that the $\mathcal{N}=5$ theory with $Sp(2N)\times O(2N)$ gauge group can
be understood as an orientifolding of the ABJM model with $U(2N)\times U(2N)$
gauge group. We briefly discuss the Type IIB brane construction of the
$\mathcal{N}=5$ theory and the geometry of the M-theory orbifold.
