This paper describes the fuzzy boundaries between support verb constructions (SVC) in Brazilian Portuguese (BP) with 'ter' ('have') and 'dar' ('give') and causative operator verb (VopC) constructions involving these same verbs. These constructions form a complex set of relations: (i) both verbs may be support verbs of the same noun; (ii) 'dar' may occur in a standard (active-like) SVC related to a converse (passive-like) SVC with 'ter'; and (iii) 'dar' may be a VopC operating on a 'ter' SVC. For 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 that represents the events (predicates) denoted by predicational nouns in SVC.