Given a set of triples of a base set $S$, find a subset of triples such that each element in $S$ appears exactly in one triple. This problem is NP-complete by reduction from NP-complete problem 3D Matching.

I'm interested in the complexity of related problem. What is the complexity of finding a subset of triples such that each element in $S$ appears exactly in two triples?

Has this problem been studied in the literature? I'd greatly appreciate pointing me to references.