  It has been recently shown that quadruply lensed gravitational-wave (GW)
events due to coalescing binaries can be localized to one or just a few
galaxies, even in the absence of an electromagnetic counterpart. We discuss how
this can be used to extract information on modified GW propagation, which is a
crucial signature of modifications of gravity at cosmological scales. We show
that, using quadruply lensed systems, it is possible to constrain the parameter
$\Xi_0$ that characterizes modified GW propagation, without the need of
imposing a prior on $H_0$. A LIGO/Virgo/Kagra network at target sensitivity
might already get a significant measurement of $\Xi_0$, while a third
generation GW detector such as the Einstein Telescope could reach a very
interesting accuracy.
