Multiplexing of projection images is a potential solution to increasing detection sensitivity in multi-pinhole (MPH) SPECT systems. However, the ambiguity caused by overlapped projections can generate artefacts in the reconstructed images. Therefore, multiplexing has been generally avoided in MPH SPECT systems at the cost of sensitivity loss. We are developing a new-generation brain-dedicated stationary SPECT scanner, AdaptiSPECT-C. In this study, we employed a prototype design of the AdaptiSPECT-C consisting of 25 square detectors arranged in a truncated spherical geometry. Each detector is equipped with an MPH collimator having 5 pinhole apertures. Each aperture can be independently opened or closed utilizing a shuttering mechanism. There is intentionally a significant amount of multiplexing when multiple apertures are opened. In this study, we propose an innovative approach to demultiplex projection data from multiple pinholes in the AdaptiSPECT-C. We used our MPH analytic simulation and iterative reconstruction software to investigate two acquisition schemes for an XCAT phantom emulating Nisopropyl-p-(I-123)iodoamphetamine (I-123-IMP) brain-perfusion agent distribution. In this approach, a small portion of imaging time (herein, 20%) is used for acquiring a set of non-multiplexed data by opening only central pinholes in each MPH collimator. The proposed algorithm can then demultiplex the projections acquired thereafter using an estimate of the activity distribution reconstructed from the non-multiplexed data. The results are promising for demultiplexing the projections when compared with simulated non-multiplexed ground truth. We expect this demultiplexing will result in substantial enhancement of the reconstructed images. This and variations in the acquisition schemes will be explored in our future studies.