It just occurred to me that were there lots of misunderstandings happening in the past when transmissions of messages could be fragmented? Like they used this word, but I don't know whether they mean X or Y because I don't know if they used A or B in the missing part of the sentence?? I'd imagine a German version of sitcoms like "Three's Company" would have very different misunderstandings than the english version
Wir treffen uns mit dem Nachbarn could work -- sich treffen is not transitive (the direct object is the reflexive pronoun and so the neighbour isn't an additional direct object).
sich mit jemandem treffen is a more deliberate meeting, while jemanden treffen can be either deliberate or a coincidental encounter.
treffen doesn't mean "hit" in the sense of "punch, strike, pummel, hit" but it can mean "hit" in the sense of "hit the target, not miss".
Context will usually tell the difference -- have you been talking about shooting guns or an archery contest or throwing rocks? If not, treffen in context will usually mean to meet, rather than to hit.
As there are many comments about the confusion of "treffen" as "(to) meet" and in the sense of "(to) hit and not to miss a target":
There is a German "Sparwitz" (kind of not-a-real-joke):
"Treffen sich zwei Jäger! - Beide tot."
This "Sparwitz" plays with the two possibilities to understand: "treffen". The first part: "Treffen sich zwei Jäger" would always be understood as "Two hunters meet." The 'result of the "meeting"': "beide tot." (=both dead) shows that they actually shot and also hit each other so you need to rethink this whole thing.