"The Spirit himself bears witness with our spirit that we are children of God." E.S.V.
There is on this site a question which looks at the meaning of the word "spirit" in this verse. Here I want to focus on "with".
Here are two "withs":
with our spirit " in attendance". Much as a jury might be involved with a case. With us listening. Good News, NET Bible, Aramaic Bible in Plain English and Douay-Rheims all put "to" our spirit. Having the sense of -The Spirit bears witness to our spirit.
The Holy Spirit bares witness with our spirit "doing the same, joining in, cooperating". A joint activity as in "I played tennis with a friend".
Maybe adding "in attendance", or, "doing the same" seeks to narrow down something which is open to possibility.
Does "with" fully represent the Greek or is it just the best English available?
Here are some possible areas for consideration in looking at the meaning of "with" in this verse.