A few that I know about --
Deuteronomy 27.14-26 A solemn warning. After verses 14-16a, the lead-reader reads each verse, through "And all the people shall say," then all, together, intone, "Amein" in solemn acknowledgment and agreement.
A happier one, but very simple antiphonal reading/prayer was done at the miqvah (baptism). Psalm 15. The reader/prayer leader reads the first verse, the ecclesia reads/prays the 2nd in answer, and the leader continues with the 3rd, while the people continue with the 4th, then all end with the 5th.
More interesting, the 118th Psalm, but I can't remember how it was done, specifically.
A fun one: Psalm 136. Joyous! At each verse, the people simply answer, "For His lovingkindness is everlasting."
And I known there are more. One, if I remember right, was upon the dedication of the new Temple, after the first one was destroyed. The people were very upset, because the new Temple was very simple, the first being to great. So they were admonished to rejoice anyway, to celebrate. They then did an antiphonal prayer/song.
There was one in which the priests went up on a hill on one side of a valley, and the people went to the other side of the valley, and they called across to each other in their song/prayer.