  The hidden order phase in URu$_2$Si$_2$ is highly sensitive to electronic
doping. A special interest in silicon-to-phosphorus substitution is due to the
fact that it may allow one, in part, to isolate the effects of tuning the
chemical potential from the complexity of the correlated $f$ and $d$ electronic
states. We investigate the new antiferromagnetic phase that is induced in
URu$_2$Si$_{2-x}$P$_x$ at $x\gtrsim0.27$. Time-of-flight neutron diffraction of
a single crystal ($x=0.28$) reveals $c$-axis collinear
$\mathbf{q}_\mathrm{m}=(\frac12,\frac12,\frac12)$ magnetic structure with
localized magnetic moments ($\approx2.1\,\mu_\mathrm{B}$). This points to an
unexpected analogy between the (Si,P) and (Ru,Rh) substitution series. Through
further comparisons with other tuning studies of URu$_2$Si$_2$, we are able to
delineate the mechanisms by which silicon-to-phosphorus substitution affects
the system. In particular, both the localization of itinerant 5$f$ electrons as
well as the choice of $\mathbf{q}_m$ appears to be consequences of the increase
in chemical potential. Further, enhanced exchange interactions are induced by
chemical pressure and lead to magnetic order, in which an increase in
inter-layer spacing may play a special role.
