  Supersymmetric theories with the same bosonic content but different fermions,
aka \emph{twins}, were thought to exist only for supergravity. Here we show
that pairs of super conformal field theories, for example exotic
$\mathcal{N}=3$ and $\mathcal{N}=1$ theories in $D=4$ spacetime dimensions, can
also be twin. We provide evidence from three different perspectives: (i) a twin
S-fold construction, (ii) a double-copy argument and (iii) by identifying
candidate twin holographically dual gauged supergravity theories. Furthermore,
twin W-supergravity theories then follow by applying the double-copy
prescription to exotic super conformal field theories.
