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.

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