I believe you're right, following this tip: https://www.grammarly.com/blog/who-vs-whom-its-not-as-complicated-as-you-might-think/ You can replace Jon with "him" but not with "he". So, to me, it's totally correct to ask "With whom?".
But if your friend says :
Your friend: Jon was there together with me.
Then you reply:
You: Who was there together with you?
But allow me to correct the two questions you might also ask. I think it's better to say :
With whom were you together? or You were together with whom?
(I don't think it's necessary to repeat "there".) And,
With whom did you want to speak? or You wanted to speak with whom?