  New local solutions in type II supergravity that are foliations of
AdS$_3\times S^3\times S^3$ over an interval and preserve at least large
$\mathcal{N}=(4,0)$ supersymmetry are found. Some cases have compact internal
space, some not and one experiences an enhancement to $\mathcal{N}=(4,4)$. We
present two new globally compact solutions with D brane and O plane sources
explicitly, one in each of IIA and IIB. The former is part of an infinite
family of solutions with D8/O8s back reacted on AdS$_3\times S^3\times
S^3\times S^1$. In the latter the the algebra degenerates to small
$\mathcal{N}=(4,0)$ and the internal geometry is bounded between D5s and O5s
back reacted on AdS$_3\times S^3\times \mathbb{R}^4$.
