We define a new dilaton Weyl multiplet of ${\mathcal{N}}=2$ conformal
supergravity in four dimensions. This is constructed by reinterpreting the
equations of motion of an on-shell hypermultiplet as constraints that render
some of the fields of the standard Weyl multiplet composite. The independent
bosonic components include four scalar fields and a triplet of gauge two-forms.
The resulting, so-called, hyper-dilaton Weyl multiplet defines a $24+24$
off-shell representation of the local ${\mathcal{N}}=2$ superconformal algebra.
By coupling the hyper-dilaton Weyl multiplet to an off-shell vector multiplet
compensator, we obtain one of the two minimal $32+32$ off-shell multiplets of
${\mathcal{N}}=2$ Poincar\’e supergravity constructed by M\”uller in 1986.
On-shell, this contains the minimal ${\mathcal{N}}=2$ Poincar\’e supergravity
multiplet together with a hypermultiplet where one of its physical scalars
plays the role of a dilaton, while its three other scalars are dualised to a
triplet of real gauge two-forms. Interestingly, a $BF$-coupling induces a
scalar potential for the dilaton without a standard gauging.
