How to dock aggregated structures comprised of "elementary" protein units like LEGO pieces?
Try DNA origami instead 

While protein assemblies are well known, rationally using proteins to assemble larger supramolecular structures is still a difficult problem:


Predicting protein folding is an unsolved problem. Sometimes even small modifications to a sequence can change the folding propensity.
Predicting protein-protein interactions is often difficult, due to challenges in understanding protein dynamics, intermolecular interactions, and accurate predictions of protein electrostatics.


There has been some progress in terms of forcing particular protein-protein assembly through intentional side-chain modification and cross-linking, and reactive end-groups (e.g protein-based metal-organic frameworks (MOFs).

That said, use of proteins for supramolecular assemblies is far harder and less prevalent than using DNA assemblies. At the moment, DNA origami is far superior for these purposes.

Edit: If you're really looking to just copy and displace atoms, I don't think you need any particular software. I'd write a Python (or other script) that reads in the PDB files, and writes out duplicate atoms displaced in the XYZ directions as needed. Group theory can help predict the angles, but you'll still need to know the protein size to work out the geometry.