To me, it seems like it could be something like "zusammenbringen" or "zusammenhalten" or utilizing "gleich" in a way. "Vereinigen" sounds more like something is united/combined to me which is why I don't think it fits according to the english meaning. Or maybe, something along the lines of "etwas zu Paar bringen"?
In English, "to pair up" would mean something along the lines of "2 independent entities working together for a common theme, while still being separate." With that in mind, that is why I think "zusammenbringen" is the closest, but it still sounds a little off.
Examples I'm thinking of:
"Lets pair up together for the group project."
"I would pair both of those words up to make it sound more natural."
"We are going to pair everyone up with a shovel to start working."
In essence, "pair together", "group up". "Versammeln" could work, but in German, that sounds more like "gather up", whereas I'm looking for something more like "pairing" together