  Using a combination of bound-state spectroscopy and loss spectroscopy, we
pinpoint eight intrastate Feshbach resonances in $^{39}$K, as well as six
previously unexplored interstate ones. We also perform a detailed
characterization of four of the intrastate resonances and two of the interstate
ones. We carry out coupled-channel scattering calculations and find good
agreement with experiment. The combination of experiment and theory provides a
faithful map of the scattering length $a$ and permits precision measurements of
the signatures of Efimov physics across four intermediate-strength resonances.
We measure the modulation of the $a^4$ scaling of the three-body loss
coefficient for both $a<0$ and $a>0$, as well as the many-body loss dynamics at
unitarity (where $a$ diverges). The absolute positions of the observed Efimov
features confirm a ubiquitous breakdown of Efimov--van-der-Waals universality
in $^{39}$K, while their relative positions are in agreement with the universal
Efimov ratios. The loss dynamics at the three broadest Feshbach resonances are
universal within experimental uncertainties, consistent with observing little
variation in the Efimov width parameters.
