The blessing of “Al HaMihya” is part of a class of blessings known as Me’enShalosh which also includes the after-blessing for wine (“Al HaGefen”) and for certain fruits from the Land of Israel (“Al HaEtz”). When one has a requisiteamount of one or more of these types of foods, one would recite all the applicable parts of Me’en Shalosh. For example, if one ate a Kazait of cake and drank a Revi’it of wine, one would recite “Al HaMihya ve’al Hakalkala ve’al HaGefen ve’al Peri HaGefen”. The Shulhan Aruch (Orah Haim 208:18) deals with a situation in which one had the requisite amount of one type of food, say cake, but not of another, like wine. In such a situation, one would only recite the appropriate part of Me’en Shalosh, in this case “Al HaMihya” and would not be permitted to add the “Al HaGefen”.
Nevertheless, Rabbi Avraham Encaoua (Kerem Hemer, Orah Haim, § 8) says that one may add a blessing to the Me’en Shalosh, even if one did not have the Halachically-required amount. Since one is reciting Me’en Shalosh anyway for food that was definitely eaten in the required amount, it gives one the opportunity to thank Hashem for other types of food that were not Halachically sufficient. It should be noted that there is not an obligation to make this addition, but rather one may added if one wishes, according to this position. Moshe Feinstein (Igrot Moshe, Orah Haim , vol. II, §109) concurs with this opinion.
Rabbi Ovadia Yosef (Hazon Ovadia, Berachot, pg. 200-201) challenges this position by saying that although one may make additions to prayer, one may not do so to blessings, and that adding “Al HaGefen” for example, would be considered a Hefsek, an interruption. Since he says that there is a disagreement in the matter, he concludes that if one consumed an amount of food that was on the lower end of opinions of the Halachically required amount, one would be able to add in the other blessing. In other words, some opinions hold that a Kezait, for example, could be as low as 18 grams and so if one had a Revi’it of wine, one would be able to add on “Al HaMihya” to the “Al HaGefen” blessing.
Summary: If one recites Me’en Shalosh after eating a requisite amount of food, there is a Halachic basis upon which to rely if one wishes to add on the appropriate part of Me’en Shalosh for other types of foods even if the requisite amount was not consumed.