By combining the thermodynamic classification of primary, secondary, and tertiary ferroics and the corresponding symmetry-allowed or symmetry-forbidden driving forces for domain switching and reorientation, with a classification of Aizu's 773 species (prototype/ferroic phase point group pairs) into 30 ensembles of property combinations, permitting to evaluate presence or absence of coupling between the different primary ferroic spontaneous quantities, symmetry conditioned possibilities of ferroic domain switching and reorientation have been evaluated. Main accent is put on cross-effects, such as magnetic field induced reorientation of antiferromagnetic, para- or diamagnetic ferroelectric and/or ferroelastic domains, and the equivalent electric field induced effects. Possibilities of poling antiferromagnetic domains have been evaluated. Examples referring to different types of ensembles are given.