A rig for connecting or disconnecting container couplers to or from the four lower corner fittings of a shipping container, the rig has two pairs of corner units held in the required transverse special relationship by a structure extending between the two corner units of each pair to form two operating end modules. A base member has sockets and/or other connectors to secure the operating end modules in a plurality of longitudinal special relationships to enable the corner units of the modules to simultaneously engage all the four lower corner fittings of a range of containers of different lengths or using different types of couplers. Each corner unit includes an indexing means for engaging and manipulating an associated coupling to connect or disconnect the coupling to or from its associated container corner fitting.
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