To reduce the number of output channels and associated cost in PET detectors, strategies to multiplex the signal channels have been investigated by several researchers. This work aims to find an optimal multiplexing strategy for detector modules consisting of a monolithic LYSO scintillator coupled to a 64-channel PMT. We apply simulated multiplexing strategies to measured data from two continuous miniature crystal element (cMiCE) detector modules. The strategies tested include standard methods such as row column summation and its variants, as well as new data-driven methods involving the principal components of measured data and variants of those components. The detector positioning resolution and bias are measured for each multiplexing strategy and the results are compared. The mean FWHM over the entire detector was 1.23 mm for no multiplexing (64 channels). Using 16 principal component channels yielded a mean FWHM resolution of 1.21 mm, while traditional row/column summation (16 channels) yielded 1.28 mm. Using 8 principal component output channels resulted in a resolution of 1.30 mm. Using the principal components of the calibration data to guide the multiplexing scheme appears to be a viable method for reducing the number of output data channels. Further study is needed to determine if the depth-of-interaction resolution can be preserved with this multiplexing scheme.