Can 'quod' refer to the previous speaker?

It is quite common to start a Latin sentence with quod, referring to the matter discussed in the previous sentence.
In a dialogue, can one use it to refer to the previous thing even if it was uttered by someone else?
That is, can the relative pronoun starting a sentence refer to another speaker and essentially mean "the thing you just said"?

Side question:
Which pronoun would be the best fit here if not the relative one?
Iste?