This paper describes the fuzzy boundaries between support verb constructions (SVC) with ter "have" and dar "give" and causative operator verb (VopC) constructions involving these same verbs, in Brazilian Portuguese (BP), which form a complex set of relations: (i) both verbs are the support verb of the same noun (SVC); (ii) dar is the standard (active-like) SVC while ter is a converse (passive-like) SVC; and (iii) dar is a VopC, operating on a ter SVC. In this paper we have systematically studied these complex relations involving SVC and VopC for BP, which constitute a challenge to Natural Language Processing (NLP) systems, and have been often ignored in related work. The paper proposes a lexically-based strategy to implement SVC in a fully-fledged, rule-based parsing system, yielding an adequate semantic structure of the events (predicates) denoted by predicative nouns in SVC.