  We study supersymmetric solutions within seven-dimensional $N=2$ gauged
supergravity coupled to three vector multiplets in seven dimensions. The gauged
supergravity contains six vector fields that gauge the $SO(4)\sim SO(3)\times
SO(3)$ symmetry and admits two $N=2$ supersymmetric $AdS_7$ vacua with $SO(4)$
and $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)$ symmetries. We consider
solutions interpolating between two asymptotically locally $AdS_7$ geometries
in the presence of a three-form field. For a particular value of the two
$SO(3)$ gauge coupling constants, the $SO(3)_{\textrm{diag}}$ supersymmetric
$AdS_7$ vacuum does not exist, but the solutions can be uplifted to eleven
dimensions by a known reduction ansatz. We also study solutions of this type
and their embedding in M-theory. We further extend these solutions to include
the $SO(3)_{\textrm{diag}}$ gauge fields and argue that, in general, this
generalization does not lead to supersymmetric solutions.
