© 2014 American Physical Society. We study three proposals for broken symmetry in the cuprate pseudogap - oxygen antiferromagnetism, ΘII orbital loop currents, and circulating currents involving apex oxygens - through numerical exploration of multiorbital Hubbard models. Our numerically exact results show no evidence for the existence of oxygen antiferromagnetic order or the ΘII 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 multiorbital Hubbard models for parameters relevant to cuprate superconductors. However, the ΘII 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.