Rif Pesachim 24a {Pesachim 110a; Chullin 86b}

HIDE/SHOW IMAGE
24a

{Pesachim 109b continues}
Ravina said: {Pesachim 110a} Each and every one is a precept in and of itself.

And the {post-Talmudic} Sages say: since each and every one is a precept in and of itself, we bless Borei Peri haGafen on each and every cup.
And they support this opinion from this that they learn {tnan - in Chullin 86b}:
One may slaughter 100 undomesticated animals in one place and perform one covering {of the blood} for all of them. 100 birds in one place and perform one covering for all of them.
Rabbi Yehuda says: If he slaughtered an undomesticated animal, he should cover, and afterwards slaughter the bird.
And we say upon it: Rabbi Yochanan said: Rabbi Yehuda admits regarding the blessing that he only blesses one blessing.
Ravina said to Rav Acha the son of Rava, and some say that Rav Acha the son of Rava said to Rav Ashi: How is this different than the incident with Rav Brona and Rav Chananel the students of Rav? -- who were sitting at a meal, and Rav Yeva the elder was acting as waiter, and they said to him, "give and we will bless," and afterwards they said to him "give to us and we will drink." Rav Yeva the Elder said to them: So said Rav: Once you say "give to us and we will bless," it is forbidden to you to drink wine.
And the response to him {why it is different}: There, drinking and blessing are impossible to co-occur. Here, it is possible for him to slaughter with one hand and cover with one hand.

We deduce now that in terms of birkat haMazon, since it is not possible to drink and bless at the same time, it is an interruption, and when he finishes birkat haMazon, he needs to make a new Borei Peri haGafen.
So too, since it is not possible to read and drink at they same time, he needs to return and bless, after he finishes the haggada and after he finishes hallel, borei peri haGafen. And it is a good reckoning, and so does one need to do.

However, regarding {the blessing after wine,} al haGefen veAl peri haGefen, there is one who maintains that one does not bless it except at the end, and there is one who maintains that one blesses it after the two cups before the meal and after the two cups after the meal.