More on SOP1 and SOP2

This paper continues [DjSh692]. We present a rank function for NSOP1 theories and give an example of a theory which is NSOP1 but not simple. We also investigate the connection between maximality in the ordering ⊳ among complete first order theories and the (N)SOP2 property. We complete the proof started in [DjSh692] of the fact that ⊳-maximality implies SOP2 and get weaker results in the other direction. The paper provides a step toward the classification of unstable theories without the strict order property.