I mean, there's no technical reason for 682 and 3812 to team up since 682 is still in a fit of omnicidal rage while 3812 gave up on a long time ago after telling his other personality "Hey man, we are above this place now, who gives a dam about this narrative anymore?" Though i guess considering how insignificant the main SCP narrative is to SCP 3812 now as he's still ascending through the verse's cosmology the only reason it wouldn't is cause 3812 wouldn't even notice or care what their doing.