Binaries in the Kuiper Belt are common. Here we present our analysis of the Solar System Origins Legacy Survey (SSOLS) to show that using a PSF-fitting method can roughly double the number of binaries identified in that dataset. Out of 198 Kuiper Belt objects (KBOs) observed by SSOLS, we find 23 to be visually separated binaries, while a further 19 are blended-PSF binaries detectable with the method we present here. This is an overall binary fraction of 21% for the SSOLS dataset of cold classical KBOs. In addition, we tested our fitting methods on synthetic data, and while we were able to show it to be very effective at detecting certain blended-PSF binary KBOs, fainter or closer binary KBOs may easily be missed, suggesting that the close binary KBO fraction could be even higher. These results strongly support the idea that most (if not all) were formed through the Streaming Instability process, and as a consequence, most KBOs were formed as near-equal mass binaries.