  Using a data set of approximately 2 million phenomenological equations of
state consistent with observational constraints, we construct new
equation-of-state-insensitive universal relations that exist between the
multipolar tidal deformability parameters of neutron stars, $\Lambda_l$, for
several high-order multipoles ($l = 5,6,7,8$). We confirm the existence of a
universal relation between the radius of the $1.4 M_\odot$ NS, $R_{1.4}$ and
the reduced tidal parameter of the binary, $\tilde{\Lambda}$, and the chirp
mass. We extend this relation to a large number of chirp masses and to the
radii of isolated NSs of different mass $M$, $R_M$. We find that there is an
optimal value of $M$ for every $\mathcal{M}$ such that the uncertainty in the
estimate of $R_M$ is minimized when using the relation. We discuss the utility
and implications of these relations for the upcoming LIGO O4 run and
third-generation detectors.
