As you can see in Shulchan Aruch, Orach Chaim 128:27 that this law - of adding another blessing - only applies while they are saying Birkat Cohanim, defined as while their hands are spread out.
To quote the Biur Halocho ibid, which the Mishna Brura and other echo:
ביאור הלכה קכ״ח:כ״ז:א׳
ואם הוסיף וכו' - לכאורה נראה דדוקא אם גם זה היה בפריסת כפים
Similarly they are allowed to repeat Birkat Cohanim in other minyanim.
So once they are finished with Birkat Cohanim and have turned back to facing the Aaron then they can add whatever blessings they wish.