With brain-dedicated multi-detector systems employing pinhole apertures the usage of detectors facing the top of the patient's head (i.e., quasi-vertex views) can provide the advantage of additional viewing from close to the brain for improved detector coverage. In this paper, we report the results of simulation and reconstruction studies to investigate the impact of the quasi-vertex views on the imaging performance of AdaptiSPECT-C, a brain-dedicated stationary SPECT system under development. In this design, both primary and scatter photons from regions located inferior to the brain can contribute to SPECT projections acquired by the quasi-vertex views, and thus degrade AdaptiSPECT-C imaging performance. In this work, we determined the proportion, origin, and nature (i.e., primary, scatter, and multiple-scatter) of counts emitted from structures within the head and throughout the body contributing to projections from the different AdaptiSPECT-C detector rings, as well as from a true vertex view detector. We simulated phantoms used to assess different aspects of image quality (i.e., uniform sphere and Derenzo), as well as anthropomorphic phantoms with multiple count levels emulating clinical(123)I activity distributions (i.e., DaTscan and perfusion). We determined that attenuation and scatter in the patient's body greatly diminish the probability of the photons emitted outside the volume of interest reaching to detectors and being recorded within the 15% photopeak energy window. In addition, we demonstrated that the inclusion of the residual of such counts in the system acquisition does not degrade visual interpretation or quantitative analysis. The addition of the quasi-vertex detectors increases volumetric sensitivity, angular sampling, and spatial resolution leading to significant enhancement in image quality, especially in the striato-thalamic and superior regions of the brain. Besides, the use of quasi-vertex detectors improves the recovery of clinically relevant metrics such as the striatal binding ratio and mean activity in selected cerebral structures.