There is a debate among the Rishonim as to the precise volume of a "Ke’zayit," the amount of food which requires the recitation of a Beracha Aharona. One view (Tosafot) identifies a "Ke’zayit" as 27-28 grams, while others (Rambam, Rif) maintain that a "Ke’zayit" is 18 grams. The Shulhan Aruch accepts the first opinion, and thus one does not recite a Beracha Aharona unless he had eaten an amount of 27-28 grams.
Rav Moshe Feinstein (1895-1986), in his Iggerot Moshe (Orah Haim, 2:109), addresses the case of a person who ate, for example, 30 grams of "Mezonot" food, such that he must recite "Al Ha’mihya," as well as, for example, 20 grams of fruit of the special species of Eretz Yisrael (grapes, figs, pomegranates, olives or dates). This person is thus clearly required to recite "Al Ha’mihya," since he ate 30 grams of "Mezonot" food, and is not required to recite "Al Ha’etz" over the fruit, since he ate less than 27 grams of fruit. However, the amount of fruit he ate does suffice to require "Al Ha’etz" according to one view among the Rishonim. The question thus becomes whether he should add the words "Al Ha’etz Ve’al Peri Ha’etz" to the Beracha he recites in order to satisfy all opinions, or if adding this phrase would constitute a "Hefsek" (impermissible interruption) in the Beracha. Rav Moshe ruled that indeed, it is proper to add "Al Ha’etz Ve’al Peri Ha’etz" in the Beracha Aharona in order to satisfy all opinions, and this addition does not constitute a "Hefsek."
This ruling also applies in the case of one who ate 30 grams of "Mezonot" food and drank a quantity of wine that requires a "Beracha Aharona" only according to some opinions. Although we follow the view that the Beracha of "Al Ha’gefen" is recited only after drinking a Rebi’it of wine, the Shulhan Aruch brings an opinion that this Beracha is recited after drinking a smaller amount – a Ke’zayit. Therefore, if a person ate an amount of "Mezonot" food that definitely requires a Beracha Aharona, and also drank a Ke’zayit, but not a Rebi’it, of wine, then he should add "Al Ha’gefen Ve’al Peri Ha’gefen" in his Beracha Aharona, in order to satisfy all opinions.
This ruling was accepted also by Hacham Ovadia Yosef, in his Hazon Ovadya – Berachot (pp. 199-202).
Another application of this ruling is a case where one ate a "Ke’zayit" of "Mezonot" food as well as a whole small grape. The Talmud Yerushalmi maintains that if a person eats a "Beriya" – a whole entity, in the form in which it grew, such as a whole grape – then he recites a Beracha Aharona regardless of the food’s size. Halacha does not follow this opinion, and therefore one who eats grapes does not recite "Al Ha’etz" unless he ate 27 or 28 grams, even if he ate a whole grape in its original form. Nevertheless, if one ate a whole grape and in any event is required to recite "Al Ha’mihya," then he should add "Al Ha’etz Ve’al Peri Ha’etz" in the Beracha in order to satisfy the view of the Yerushlami.
Rav Yisrael Bitan notes this Halacha in the English edition of Yalkut Yosef – Berachot (p. 220). He adds, though, that it is clearly preferably to avoid this situation, and not eat a quantity of food that requires a Beracha Aharona according to some opinions but not according to others.
Summary: The minimum amount of food that must be eaten for a Beracha Aharona to be required is 27-28 grams. Some opinions require a Beracha Aharona after eating just 18 grams, but Halacha does not follow this view. Nevertheless, if a person ate between 18-27 grams of a fruit from the special species – for example, dates – and he must in any event recite "Al Ha’mihya," then he should include the words "Al Ha’etz Ve’al Peri Ha’etz" in his Beracha, in order to satisfy all opinions.