Guanine-rich DNA repeat sequences located at the terminal ends of chromosomal DNA can fold in a sequence-dependent manner into G-quadruplex structures, notably the terminal 150-200 nucleotides at the 3' end, which occur as a single-stranded DNA overhang. The crystal structures of quadruplexes with two and four human telomeric repeats show an all-parallel-stranded topology that is readily capable of forming extended stacks of such quadruplex structures, with external TTA loops positioned to potentially interact with other macromolecules. This study reports on possible arrangements for these quadruplex dimers and tetramers, which can be formed from 8 or 16 telomeric DNA repeats, and on a methodology for modeling their interactions with small molecules. A series of computational methods including molecular dynamics, free energy calculations, and principal components analysis have been used to characterize the properties of these higher-order G-quadruplex dimers and tetramers with parallel-stranded topology. The results confirm the stability of the central G-tetrads, the individual quadruplexes, and the resulting multimers. Principal components analysis has been carried out to highlight the dominant motions in these G-quadruplex dimer and multimer structures. The TTA loop is the most flexible part of the model and the overall multimer quadruplex becoming more stable with the addition of further G-tetrads. The addition of a ligand to the model confirms the hypothesis that flat planar chromophores stabilize G-quadruplex structures by making them less flexible.