  We find a sixteen supersymmetric mass-deformed Bagger-Lambert theory with
$SO(4)\times SO(4)$ global R-symmetry. The R-charge plays the `non-central'
term in the superalgebra. This theory has one symmetric vacuum and two
in-equivalent broken sectors of vacua. Each sector of the broken symmetry has
the SO(4) geometry. We find the 1/2 BPS domain walls connecting the symmetric
phase and any broken phase, and 1/4 BPS supertube-like objects, which may
appear as anyonic q-balls in the symmetric phase or vortices in the broken
phase. We also discuss mass deformations which reduces the number of
supersymmetries.
