We have analyzed the coupled-collective mode spectrum of a periodic superlattice (SL) of one-dimensional (1D) quantum wires in interaction with the background local plasma. Based on reasonable approximations we have given analytical results for the modes by showing explicitly how, in the extreme strong coupling limit, the 1D SL tends to change character to become a single 2D electron layer, and how, in the extreme weak coupling limit, the SL wire system reduces to an isolated single wire. We have also analyzed the mode coupling of the bulk (3D) plasmon and the lower-dimensional (2D/1D) plasmons in the appropriate limits.