is a potential Kitaev magnet with a monoclinic layered crystal structure. Recent investigations of the -symmetric sister compound have uncovered a unique triple- magnetic ground state, as opposed to a single- (zigzag) one, prompting us to examine the influence of the reduced structural symmetry of on its ground state. Neutron diffraction data obtained on a twin-free crystal reveal that the ground state remains a multi- state, despite the system's strong non--symmetric anisotropy. This robustness of multi- orders suggests that they are driven by a common mechanism in the honeycomb cobaltates, such as interactions beyond the bilinear order. Spin-polarized neutron diffraction results show that the ordered moments are entirely in plane, with each staggered component orthogonal to the propagating wave vector. The inferred ground state appears more compatible with the so-called XXZ easy-plane anisotropy than the Kitaev anisotropy, and features unequal ordered moments reduced by strong quantum fluctuations.