  Supersymmetric and non-supersymmetric deformations of large $N=(4,4)$ SCFT
with superconformal symmetry $D^1(2,1;\alpha)\times D^1(2,1;\alpha)$ are
explored in the gravity dual described by a Chern-Simons $N=8$, $(SO(4)\times
SO(4))\ltimes \mathbf{T}^{12}$ gauged supergravity in three dimensions. For
$\alpha>0$, the gauged supergravity describes an effective theory of the
maximal supergravity in nine dimensions on $AdS_3\times S^3\times S^3$ with the
parameter $\alpha$ being the ratio of the two $S^3$ radii. We consider the
scalar manifold of the supergravity theory of the form $SO(8,8)/SO(8)\times
SO(8)$ and find a number of stable non-supersymmetric $AdS_3$ critical points
for some values of $\alpha$. These correspond to non-supersymmetric IR fixed
points of the UV $N=(4,4)$ SCFT dual to the maximally supersymmetric critical
point. We study the associated RG flow solutions interpolating between these
fixed points and the UV $N=(4,4)$ SCFT. Possible supersymmetric flows to
non-conformal field theories are also investigated. Additionally, a
half-supersymmetric domain wall within this gauged supergravity is obtained.
