In order to say Birchas Hamazon with a mezuman, the people in the mezuman must eat together. Maran Rav Yosef Shalom Elyashiv shlita points out two cases on Pesach night when people eating together do not qualify for a mezuman and must say Birchas Hamazon as individuals without a mezuman.
The first is two people who eat the seder together, but one uses only machine matzoh while the other only eats hand matzoh. Despite the fact that this is only a chumrah and technically, l’halacha, each one is permitted to eat the other one’s matzoh, nevertheless, they are not considered eating together for the sake of zimun.
The second case is people who eat the seder together but each one eats their own food and they have a minhag not to eat from anyone else’s food other than their own. Here also, says Rav Elyashiv, they cannot make a zimun together.
(Kovetz Tel Talpiyos – Piskei Shmu’os Pesach)