In PET detector designs, the scintillator material can be partitioned such that a block of crystals share timing/energy readout electronics. A fraction of the incident 511 keV photons produce simultaneous events in two adjacent block readout channels due to Compton scattering of photons from the primary block into an adjacent block. These inter-block Compton scatter events are typically not processed in current PET scanners. We demonstrated experimentally that inter-block Compton events may be recovered as valid events with a corrected time stamp and estimated position of initial interaction in a pair of adjacent 164825 mm LYSO blocks. The recovery process resulted in a block sensitivity improvement of 5% at the expense of a small (2%) degradation in the average coincidence resolving time of each block. Implementation of the recovery procedure on a ToF-PET scanner constructed using such blocks is expected to result in an overall scanner sensitivity improvement of 20% without significant processing overhead.