  We consider the notion of strong self-absorption for continuous actions of
locally compact groups on the hyperfinite II$_1$-factor and characterize when
such an action is tensorially absorbed by another given action on any separably
acting von Neumann algebra. This extends the well-known McDuff property for von
Neumann algebras and is analogous to the core theorems around strongly
self-absorbing C$^*$-dynamics. Given a countable discrete group $G$ and an
amenable action $G\curvearrowright M$ on any separably acting semi-finite von
Neumann algebra, we establish a type of measurable local-to-global principle:
If a given strongly self-absorbing $G$-action is suitably absorbed at the level
of each fibre in the direct integral decomposition of $M$, then it is
tensorially absorbed by the action on $M$. As a direct application of Ocneanu's
theorem, we deduce that if $M$ has the McDuff property, then every amenable
$G$-action on $M$ has the equivariant McDuff property, regardless whether $M$
is assumed to be injective or not. By employing Tomita-Takesaki theory, we can
extend the latter result to the general case where $M$ is not assumed to be
semi-finite.
