  We present post-jet-break \textit{HST}, VLA and \textit{Chandra} observations
of the afterglow of the long $\gamma$-ray bursts GRB 160625B (between 69 and
209 days) and GRB 160509A (between 35 and 80 days). We calculate the
post-jet-break decline rates of the light curves, and find the afterglow of GRB
160625B inconsistent with a simple $t^{-3/4}$ steepening over the break,
expected from the geometric effect of the jet edge entering our line of sight.
However, the favored optical post-break decline ($f_{\nu} \propto t^{-1.96 \pm
0.07}$) is also inconsistent with the $f_{\nu} \propto t^{-p}$ decline (where
$p \approx 2.3$ from the pre-break light curve), which is expected from
exponential lateral expansion of the jet; perhaps suggesting lateral expansion
that only affects a fraction of the jet. The post-break decline of GRB 160509A
is consistent with both the $t^{-3/4}$ steepening and with $f_{\nu} \propto
t^{-p}$. We also use {\sc boxfit} to fit afterglow models to both light curves
and find both to be energetically consistent with a millisecond magnetar
central engine, although the magnetar parameters need to be extreme (i.e. $E
\sim 3 \times 10^{52}$ erg). Finally, the late-time radio light curves of both
afterglows are not reproduced well by {\sc boxfit} and are inconsistent with
predictions from the standard jet model; instead both are well represented by a
single power law decline (roughly $f_{\nu} \propto t^{-1}$) with no breaks.
This requires a highly chromatic jet break ($t_{j,\mathrm{radio}} > 10 \times
t_{j,\mathrm{optical}}$) and possibly a two-component jet for both bursts.
