The present paper can be seen as a sequel to [\textit{F. Berchtold} and \textit{J. Hausen}, Mich. Math. J. 54, No. 3, 483--515 (2006; Zbl 1171.14028)]. Again, good quotients are under investigation -- but now the authors are not restricted to quasiprojective ones. Moreover, the action of an arbitrary reductive group \(G\) on a Mori Dream Space \(X\) is considered. The goal is to describe the so-called good \(G\)-sets, i.e.\ those open, \(G\)-invariant \(U\subseteq X\) admitting a good quotient \(U/\!\!/ G\). Starting again from the well known situation of a torus action on a factorial, affine variety \(Z\), the authors recall that all maximal good \(T\)-sets arise from characters of the trivial bundle. As in [loc. cit.], the chambers of the GIT fan describe the quasiprojective quotients. However, the more general quotients correspond to more complicated collections of weight cones in the character group of the torus \(T\). This result can now be lifted to the case of a reductive group \(G\) by studying the torus \(T:=G/[G,G]\). It has the same character group as \(G\), and \(T\) acts on the affine, factorial \(Y=X/\!\!/ [G,G]\). Moreover, good \(G\)-sets in \(X\) are in bijection to good \(T\)-sets in \(Y\) -- and they provide the same quotients. Finally, to investigate quotients of more general (non-affine) varieties \(X\), the action of \(G\) is lifted to the (finitely generated) Cox ring. In principle, this works as in [loc. cit.] -- but the lack of quasiprojectivity of the quotients requires some additional effort. As a reward for this, the authors obtain another application. They develop a general theory about the commutation of taking good quotients by several groups. In particular, they provide a general framework for the Gelfand MacPherson correspondence relating quotients of the Grassmanians by the ambient torus with quotients of configuration spaces by the linear group.