If three people eat a meal together, and one finishes his meal and wishes to leave, he must wait until the other two are ready to recite Birkat Hamazon, so they can recite a Zimun. The one participant who wishes to leave cannot force the other two to interrupt their meal so that he can recite a Zimun. He must rather wait for them to finish. Of course, if the other two agree to interrupt for a Zimun, they may, and they resume eating after the Zimun.
If, however, two of the three participants wish to leave, they – as the majority of the group – may force the third to stop eating and join them in a Zimun, after which he may resume eating. According to the Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), the individual may not resume eating until after the other two complete the first Beracha of Birkat Hamazon ("Ha’zan Et Ha’kol"). Hacham Ovadia Yosef, however, maintains that he may resume his meal immediately upon the completion of the Zimun, that is, once the leader of the Zimun repeats the blessing, "Baruch She’achalnu Mi’shelo…"
If four people eat together, and one of them wishes to leave, then, as mentioned, he may not force the others to interrupt for a Zimun, but they certainly may volunteer to do so. In such a case, the three who continue eating after the Zimun do not recite a new Zimun when they finish eating. Even though they comprise the minimum required quorum for a Zimun, they do not recite a Zimun since only one Zimun is recited at each meal. The exception to this rule, as the Ben Ish Hai notes, is the interesting case where ten people eat together, three of whom wish to leave before the other seven, and the other seven agree to interrupt their meal so a Zimun can be recited with God’s Name. (When ten people recite a Zimun together, they do add God’s Name – "Elokenu" – to the text of the Zimun.) When the remaining seven men complete their meal and are ready for Birkat Hamazon, they may recite an additional Zimun. Since the three who recited Birkat Hamazon constituted an independent group with respect to Zimun, in that they could have formed their own Zimun (albeit without God’s Name), the other seven likewise are seen as a separate group, and can form an additional Zimun. Of course, they do not recite God’s Name in the Zimun, since they are fewer than ten people.
In conclusion, it should be noted that the Ben Ish Hai discouraged the practice of interrupting one’s meal to recite a Zimun with those who wish to leave. There were some authorities who held that once a person interrupts his meal to take part in a Zimun, he must recite new Berachot over his food when he resumes eating. Although Halacha does not follow this opinion, it is preferable to avoid a situation of disagreement among the authorities concerning the recitation of Berachot. The Ben Ish Hai therefore urged people to wait until all participants of the meal have finished eating before reciting a Zimun.
Summary: If three people eat a meal together, and two people wish to leave, they can force the third to interrupt his meal to recite a Zimun, and he may resume eating immediately after the Zimun. In the converse case, one individual may not force the other two to interrupt their meal for a Zimun, though they may volunteer to do so. If four people eat together and three of them interrupt their meal to recite a Zimun for the fourth, who wishes to leave, the remaining three do not recite an additional Zimun when they finish eating. However, if ten people eat together and seven of them interrupt their meal to recite a Zimun with the three others, who wish to leave, the remaining seven recite a second Zimun when they finish eating.
