  We consider genuine type IIB string theory (supersymmetric) brane
intersections that preserve $(1+1)$D Lorentz symmetry. We provide the full
supergravity solutions in their analytic form and discuss their physical
properties. The Ansatz for the spacetime dependence of the different brane warp
factors goes beyond the harmonic superposition principle. By studying the
associated near-horizon geometry, we construct interesting classes of AdS$_3$
vacua in type IIB and highlight their relation to the existing classifications
in the literature. Finally, we discuss their holographic properties.
