We consider “twin supergravities”—pairs of supergravities with
N
+
and
N
−
supersymmetries,
N
+
>
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 ones. In particular, the matter coupled
N
−
twins in
D
=
3
, 5, 6 and the
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 bifundamental scalar that couples to the well-known biadjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorization into left and right super Yang-Mills-matter theories.