  In dimension $n=3$, there is a complete theory of weak solutions of Ricci
flow - the singular Ricci flows introduced by Kleiner and Lott - which are
unique across singularities, as was proved by Bamler and Kleiner. We show that
uniqueness should not be expected to hold for Ricci flow weak solutions in
dimensions $n\geq5$. Specifically, we exhibit a discrete family of
asymptotically conical gradient shrinking solitons, each of which admits
non-unique forward continuations by gradient expanding solitons. (v2) We recast
the Main Theorem in the language of Kleiner and Lott's Ricci Flow spacetimes
and in addition show that topological nonuniqueness is possible for the
solutions we construct.
