We construct new families of $$ \mathcal{N} $$
N
= (0, 4) AdS3 × S2 × $$ {\tilde{S}}^2 $$
S
˜
2
× S1 backgrounds fibred over a 2d Riemann surface in Type IIB string theory. These solutions are obtained by extracting the near-horizon limit of D3-brane box configurations, consisting of D3-D5-NS5 branes ending on D5′-NS5′ background branes. We relate our families of solutions to previous AdS3 × S2 × CY2 and AdS3 × S3 × S2 solutions to Type IIA recently constructed in the literature. We construct explicit 2d quiver CFTs associated to the D3-brane box configurations, and check that the central charges match the holographic result. We extend our solutions to include D7-branes, and show that a subclass of these solutions can be interpreted in terms of D3-D5-NS5 defect branes embedded in a 5d fixed point theory. This is explicitly realised by linking our solutions to a 6d domain wall that asymptotes locally the AdS6 × S2 × Σ2 solution T-dual to the Brandhuber-Oz vacuum.