  We have studied systematically the influence of particle-hole symmetric and
asymmetric kinetic terms on the ordered phases that we may observe competing or
coexisting in a tetragonal system. We show that there are precise patterns of
triplets of ordered phases that are accessible (i.e. it is impossible to
observe two of them without the third one). We found a systematic way to
predict these patterns of states and tested it by identifying at least 16
different patterns of three order parameters that necessarily coexist in the
presence of the kinetic terms. We show that there are two types of general
equations governing the competition of all these triplets of order parameters
and we provide them.
