The Rosh states in the name of Rabbeinu Chananel that it is implicit from our Gemora that one is not allowed to eat before Mussaf for otherwise, the kohanim might get drunk before Mussaf as well.
Shulchan Aruch (O”C 286:3) rules that it is permitted to taste fruit or a little bread prior to davening Mussaf. However, eating a meal is prohibited. This would be consistent with the opinion of the Rosh.
The Bach writes that from the language of the Shulchan Aruch, he can infer that there is no prohibition against eating prior to Mussaf; rather, it has become an accepted practice and therefore drunkenness is not so common. According to the Bach, if one would be weak and he appraises that he cannot daven Mussaf without eating, he would be permitted to eat since it is only a custom not to eat.
In the sefer Shoel U’meishiv (3,1:120), he comments on the custom of some communities, where they refrain from eating prior to shaking the lulav on Sukkos. They daven Shacharis and Hallel early in the morning and then they go home to eat and afterwards return to the Shul to daven Mussaf. The Shoel U’meishiv objects to this because they are now eating before Mussaf. He writes, however, that he remembers in the year 5597, in the city of Nikolsburg, he witnessed people davening every Shabbos morning until the Torah reading, going home to eat and afterwards returning to daven Mussaf in the tenth hour of the day. When he asked them to explain this custom, they responded that the Gaon Rav Mordechai Bennet ruled that they had permission to do so since they were weak and desired to eat. This ruling is seemingly based on the Bach who maintains that there is no actual prohibition regarding eating prior to Mussaf, rather it is only a custom and therefore it can be overridden.
There are many communities where it has become the custom for the entire congregation to recite kiddush and eat a little prior to Mussaf. Rav Shmuel Rosenberg, the Av Beis Din in Unsdorf was asked if it was permitted for an individual to separate from the tzibur and daven Mussaf while everyone is making kiddush and only then would he eat. He rules that the custom of not eating prior to reciting Mussaf is an established custom and there have been many G-d fearing Torah scholars who refrain from eating prior to davening Mussaf. We cannot object to someone who wants to be stringent on himself in this regard. Furthermore, since Shulchan Aruch rules that only tasting is permitted and not an eating which will cause satiation, who can be so meticulous to discern the amount in which he is eating.
There is an argument amongst the poskim as to the amount of food that one is permitted to eat prior to davening Mussaf. Some rule that there is no set amount that is prohibited, providing that he is not eating a meal that would require Birchas Hamazon afterwards. According to this, one would be allowed to eat cake and drink coffee before he davens Mussaf. The Mishna Berura’s opinion is that one should not eat cake that measures more than the size of an egg. It is brought in the name of Rav Shlomo Zalman Auerbach that the custom is to be lenient and one has who to rely on if he will eat cake that measures more than the size of an egg prior to davening Mussaf. (Peninei Halacha)