This is the kind of idiomatic quirk which drives no-English speakers crazy. But, yes, it can definitely be pluralised.

I was hearing 'reaching out' on US TV shows such as NYPD Blue 20 years ago. The cops would use it to describe the process of contacting someone with whom they'd previously had no relationship or trying to re-establish a rapport with someone who was now more distant or estranged. It was usually used in the context of getting help or assistance.