  We construct Type IIB string theory setups which, via double holography,
realize two gravitational systems in separate AdS spaces which interact with
each other and with a non-gravitational bath. We employ top-down string theory
solutions with concrete field theory duals in the form of 4d $\mathcal N=4$ SYM
BCFTs and a first-principles notion of double holography. The setups are used
to realize pairs of `near' and `far' black holes from the perspective of the
bath, which exchange Hawking radiation with each other and radiate into the
bath. We identify three phases for the entropy in the bath characterized as no
island, partial island and full island, and discuss the entropy curves. The
setups differ from the black hole binaries observed in gravitational wave
experiments but may capture certain aspects.
