  We study three proposals for broken symmetry in the cuprate pseudogap -
oxygen antiferromagnetism, $\Theta_{II}$ orbital loop currents, and circulating
currents involving apex oxygens - through numerical exploration of
multi-orbital Hubbard models. Our numerically exact results show no evidence
for the existence of oxygen antiferromagnetic order or the $\Theta_{II}$ phase
in the three-orbital Hubbard model. The model also fails to sustain an ordered
current pattern even with the presence of additional apex oxygen orbitals. We
thereby conclude that it is difficult to stabilize the aforementioned phases in
the multi-orbital Hubbard models for parameters relevant to cuprate
superconductors. However, the $\Theta_{II}$ phase might be stabilized through
explicit flux terms. We find an enhanced propensity for circulating currents
with such terms in calculations simulating applied stress or strain, which skew
the copper-oxygen plane to resemble a kagome lattice. We propose an
experimental viewpoint to shed additional light on this problem.
