This study proposes a multi-radar system for non-contact physiological sensing across arbitrary body orientations. In integrating signals obtained from different radar viewpoints, we adopt a multivariate variational mode decomposition method to extract the common respiratory component. Experiments conducted with six subjects under varying distances and orientations demonstrate that, compared with a single-radar setup, the proposed system reduced the root mean square error of the respiratory interval by 35.5%, decreased the mean absolute error of the respiratory rate by 30.8%, and improved accuracy by 9.4 percentage points. These results highlight that combining multiple radar viewpoints with signal integration enables stable respiratory measurement regardless of body orientation.