Ligand exchange is a much-used method to increase the conductivity of colloidal quantum-dot films by replacing long insulating ligands on quantum-dot surfaces with shorter ones. Here we show that while some ligands indeed replace the original ones as expected, others may be used to controllably remove the native ligands and induce epitaxial necking of specific crystal facets. In particular, we demonstrate that amines strip lead oleate from the (100) surfaces of PbSe quantum dots. This leads to necking of QDs and results in cubic superlattices of epitaxially connected QDs. The number of amine head-groups as well as the carbon chain length of linear diamines is shown to control the extent of necking. DFT calculations show that removal of Pb(oleate)2 from (100) surfaces is exothermic for all amines, but the driving force increases as monoamines < long diamines < short diamines < tetramines. The neck formation and cubic ordering results in a higher optical absorption cross section and higher charge carrier mobilities, thereby showing that the use of the proper multidentate amine molecules is a powerful tool to create supercrystals of epitaxially connected PbSe QDs with controlled electronic coupling.