  Whether or not a physical property can be enhanced in an inhomogeneous system
compared with its homogeneous counterpart is an intriguing fundamental
question. We provide a concrete example with positive answer by uncovering a
remarkable enhancement of both antiferromagnetic (AF) structure factor and
$d$-wave pairing tendency in the doped staggered periodic Anderson model (PAM)
with two alternating inequivalent local moments. The common thread of these
enhancement is found to originate from the generic "self-averaging" effect and
non-monotonic dependence of the corresponding physical quantity in homogeneous
PAM. More strikingly, we provided evidence of the coexistence of these two
enhancement via a tentative phase diagram. Our findings may imply the plausible
generalization of enhancing physical properties in generic inhomogeneous
systems.
