When should a mezuman use a cup of wine?

Hi,

There is an ancient practice of having the leader of a mezuman conclude the birkat hamazon blessing after meals with a blessing upon a cup of wine [or grape juice] (kos shel berachah). This is not considered obligatory; indeed, today some consider it less than appropriate because our mezuman is not a true mezuman. The original form of mezuman involved the leader reciting birkat hamazon on behalf of the listeners, and we have each individual recite birkat hamazon independently.

Some particularly have the leader of the mezuman recite the concluding blessing upon a cup on Shabbat or Yom Tov. Since this is a way to beautify the mitzvah, it is most appropriate for a beautiful day - Shabbat and Yom Tov.

(Rivivot Ephraim 1:150:6)

Have a great day,
Mordechai