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 ($f_{ u} propto t^{-1.96 pm 0.07}$) is also inconsistent with the $f_{ u} propto t^{-p}$ 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 $f_{ u} propto t^{-p}$. 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 $f_{ u} propto t^{-1}$) 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.
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