Sedimentary basins strongly affect earthquake ground motions of both body and surface waves that propagate through them. Yet to characterize seismic hazards at a specific site, it is common practice to consider only the effects of near-surface geology on vertically propagating body waves despite surface waves often causing strong damage. Recently, Bowden & Tsai (2017) proposed an semi-analytical method to predict surface-wave basin amplification and noticed that certain large regional earthquake ground motions are under-predicted if surface waves are not properly accounted for. Since the theory is based on a 1-D approximation of the near-surface geologic structure and does not account for path effects, it is of interest to know how significantly such additional complexity affects the 1-D predictions. When considering deep basins, several other basin parameters play a role in the amplification of surface waves: transmission and conversion at the basin edge, basin shape, lateral resonance and focusing effects. As surface waves propagate back and forth in a highly dispersive medium, the amplification also varies strongly from the edge to the center of the basin. These effects are not always accounted for because of the cost of geophysical surveys that would accurately constrain the structure, the lack of earthquake data for empirical predictions, the poor understanding of what main factors are responsible for basin amplification, and the absence of quantitative estimates of their contribution to the overall amplification. The current study aims to provide quantitative estimates of the importance of these various path effects on surface waves amplification and also extend the current 1-D theory to more complex multi-dimensional basin structures.