Multi-pinhole collimators are often used in pre-clinical SPECT systems because they have a better resolution-sensitivity tradeoff than parallel hole collimators when imaging small objects. Most multi-pinhole collimators are designed to allow no or only a limited amount of overlap between the different pinhole projections because the ambiguity introduced by multiplexing pinholes can result in artifacts. The origin of these artifacts is still not fully understood, but previous research has already shown that data incompleteness could be part of the explanation. Therefore, we developed a method to investigate data completeness in multiplexing multi-pinhole systems and showed that a certain activity distribution can be successfully reconstructed when the nonmultiplexed data is complete or when the overlap can be sufficiently de-multiplexed. We validated this method using computer simulated phantom data of different multiplexing systems. We also studied contrast-to-noise and nonprewhitening matched filter signal-to-noise ratio (NPW-SNR) to compare the image quality in a single pinhole system with multiplexing systems. We found that our method can indeed be used to evaluate data completeness in multiplexing systems and found no artifacts in the systems that had complete data. Sensitivity increased significantly with multiplexing but we found only small, nonsignificant differences in contrast-to-noise ratio. However, the NPW-SNR did slightly improve in the multiplexing setups. We conclude that more multiplexing does not necessarily result in more artifacts and that even a high amount of multiplexing can still result in artifact-free images if the nonmultiplexed data is complete or when the overlap can be sufficiently de-multiplexed.