Wild theories with o-minimal open core

Let T be a consistent o-minimal theory extending the theory of densely ordered groups and let $T^{\prime }$ be a consistent theory. Then there is a complete theory $T^{?}$ extending T such that T is an open core of $T^{?}$, but every model of $T^{?}$ interprets a model of $T^{\prime }$. If $T^{\prime }$ is NIP, $T^{?}$ can be chosen to be NIP as well. From this we deduce the existence of an NIP expansion of the real field that has no distal expansion.