  I first isolate a hierarchy of axioms over ZFC that allows a proper class of
urelements. The Collection Principle and Reflection Principle hold precisely
when the urelements are arranged in a specific manner. I then turn to forcing
with urelements. A new forcing machinery with urelements is proposed to address
a problem with the existing approach regarding the property of fullness. Every
new forcing relation is full just in case Collection holds in the ground model.
Forcing with urelements can preserve, destroy, or recover various axioms within
the hierarchy. Ground model definability fails when the ground model contains a
proper class of urelements.
