In marketing channels processing rules, the value of the channel can be set to only one dimension no matter how many conditions are in the processing rules. So if you want to set social to the value of the referring domain, you cannot set it to the value of cmp string in cases where there is no referring domain.
Please consider this as an option.
Ben Gaines says there's no way to do this now, but it would be a good idea. See the tweet exchange below.