Hydrogen, halogen, lithium and beryllium bonding are briefly surveyed as a prelude to a report of a computational study of the interplay between these various non-covalent interactions. Our study used model dimers and trimers involving the thiirane molecule, (CH2)2S, complexed with small molecules like HF, ClF, BrF, LiF and BeH2 to assess and investigate the interplay between the different non-covalent interactions. The model trimer systems show positive cooperative effects when thiirane is one of the terminal molecules, whereas a negative cooperative effect is evident when it is at the center of the trimer. The changes in selected molecular properties, including the redistribution of charge densities obtained by the natural population analysis (NPA), implemented in the natural bond orbital (NBO) procedure, and an Atoms in Molecules (AIM) topological analysis, were useful in understanding these cooperative effects.