  Observations of the properties of multiple coalescing neutron stars will
simultaneously provide insight into neutron star mass and spin distribution,
the neutron star merger rate, and the nuclear equation of state. Not all
merging binaries containing neutron stars are expected to be identical.
Plausible sources of diversity in these coalescing binaries can arise from a
broad or multi-peaked NS mass distribution; the effect of different and extreme
NS natal spins; the possibility of NS-BH mergers; or even the possibility of
phase transitions, allowing for NS with similar mass but strongly divergent
radius. In this work, we provide a concrete algorithm to combine all
information obtained from GW measurements into a joint constraint on the NS
merger rate, the distribution of NS properties, and the nuclear equation of
state. Using a concrete example, we show how biased mass distribution
inferences can significantly impact the recovered equation of state, even in
the small-$N$ limit. With the same concrete example, we show how small-$N$
observations could identify a bimodal mass and spin distribution for merging NS
simultaneously with the EOS. Our concordance approach can be immediately
generalized to incorporate other observational constraints.
