This article addresses the problem that the expressive power of tree-adjoining grammars (TAGs) is too limited to deal with certain syntactic phenomena, in particular, with scrambling in free-word-order languages. The TAG variants proposed so far in order to account for scrambling are not entirely satisfying. Therefore, the article introduces an alternative extension of TAG that is based on the notion of node sharing, so-called (restricted) tree-local multicomponent TAG with shared nodes (RSN-MCTAG). The analysis of some German scrambling data is sketched in order to show that this TAG extension can deal with scrambling. Then it is shown that for RSN-MCTAGs of a specific type, equivalent simple range concatenation grammars can be constructed. As a consequence, these RSN-MCTAGs are mildly context-sensitive and in particular polynomially parsable. These specific RSN-MCTAGs probably can deal not with all scrambling phenomena, but with an arbitrarily large subset.