  We consider `twin supergravities' - pairs of supergravities with
$\mathcal{N}_+$ and $\mathcal{N}_-$ supersymmetries,
$\mathcal{N}_+>\mathcal{N}_-$, with identical bosonic sectors - in the context
of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of
twin supergravity theories are related through their left and right super
Yang-Mills factors. This procedure generates new theories from old. In
particular, the matter coupled $\mathcal{N}_-$ twins in $D=3,5,6$ and the
$\mathcal{N}_-=1$ twins in $D=4$ have not, as far as we are aware, been
obtained previously using the double-copy construction, adding to the growing
list of double-copy constructible theories. The use of fundamental matter
multiplets in the double-copy construction leads us to introduce a
bi-fundamental scalar that couples to the well-known bi-adjoint scalar field.
It is also shown that certain matter coupled supergravities admit more than one
factorisation into left and right super Yang-Mills-matter theories.
