These extra actions allow the parser to link to nodes that are several positions deep in the stack, creating non-projective links.
in particular, Attardi uses six non-projective actions: two actions to link to nodes that are two positions deep, another two actions for nodes that are three positions deep, and a third pair of actions that generalizes the previous ones to n positions deep for any n. the maximum depth in the stack to which links can be created can be configured according to the actions allowed.