The interplay and coexistence of superconducting, magnetic, and structural order parameters in NaFeCoAs have been studied using superconducting quantum interference device magnetometry, muon spin rotation, and synchrotron x-ray powder diffraction. Substituting Fe by Co weakens the ordered magnetic state through both a suppression of and a reduction in the size of the ordered moment. Upon further substitution of Fe by Co the high sensitivity of the muon as a local magnetic probe reveals a magnetically disordered phase, in which the size of the moment continues to decrease and falls to zero around the same point at which the magnetically driven structural distortion is no longer resolvable. Both magnetism and the structural distortion are weakened as the robust superconducting state is established.