上で

on; in or at a place, surface, or medium, after doing; once ... has been done

→ 上
phrase Common #4,307
on; in or at a place, surface, or medium Used after a noun to indicate where something happens or is located.
JA: ステージ上で彼女の歌を聴いたことがありますか?
EN: Have you ever heard her sing on stage?

上で生まれるんだ

It’s born up above.

— 君たちはどう生きるか (2023)

マイルス・デイビスがこの上でおしっこしたと言ったら?

What if I told you Miles Davis peed on this?

— ラ・ラ・ランド (2016)

二人ともあの上で何をやってたの?

What were you two doing up there?

phrase Rare #30,781
after doing; once ... has been done Used when one action is completed before taking the next step, often after careful consideration or preparation.
JA: あなたの申し出はよく調べた上でご返事しましょう。
EN: I’ll reply after carefully looking into your offer.

我々は十分調べた上でそう言ってるんですがね

We're saying that after doing our due diligence, you know.

— 生きる (1952)

あることを理解して貰った上で君に頼みたいことがある

Now that you understand that, there's something I'd like to ask you.

— GHOST IN THE SHELL (1995)

私のことよく分かった上で、私のことどう思う?

Now that you know me well, what do you think of me?

あなたの申し出はよく調べた上でご返事しましょう。

I’ll carefully consider your offer before giving you my answer.

多くの買い物は注意深く考えた上で行われている。

Most purchases are made after careful consideration.

間違いを訂正した上で、ファイルをルクセンバーグ氏に返却して下さい。

After correcting the mistakes, please return the file to Mr. Luxemburg.