  The hidden order phase in \urusi~is highly sensitive to electronic doping. A
special interest in silicon-to-phosphorus substitution is due to the fact that
it may allow 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 colinear
$\mathbf{q}_\mathrm{m}=(\frac12,\frac12,\frac12)$ magnetic structure with
localized magnetic moments ($\approx2.1\,\mu_\mathrm{B}$). This reveals an
unexpected analogy between the (Si,P) and (Ru,Rh) substitution series. Through
further comparisons with other tuning studies of \urusi, 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.
