In the linguistics literature, it has been generally agreed that long-distance binding of ziji becomes unavailable if a 1st/2nd person blocker is employed: 1st/2nd person blocking effects. Recently, it turns out that several linguistic factors may give an influence to this effect; hence non-cannonical patterns arise. Focusing on the Agree-based analysis, this paper discusses how those patterns can be explained in a unified way. Especially, we examine the nature of several unexpected patterns by pursuing answers to the questions like (i) why a significant number of Chinese speakers appears not to be sensitive to such blocking, or (ii) why an opposite pattern is even observed given that ziji resists to be co-indexed with a 1st/2nd person non-local antecedent. Concomitantly, it is briefly discussed how discourse-based approaches can be collaborated with the syntactic approaches.