Bereishis Rabbah 50:2 states that one angel cannot perform multiple tasks:
אין מלאך אחד עושה שתי שליחות ולא שתי מלאכים עושים שליחות אחד.
One angel cannot perform two agencies, nor can two angels perform a single agency.
Yet Eichah Rabbah 2:3 states that Gavriel performed three agencies:
אמר רבי יוחנן למלאך קשה שביניהם אמר זה גבריאל שנאמר ואיש אחד בתוכם לבש בדים וקסת בספר במתניו. ג׳ דברים היה אותו מלאך משמש קסנטור ספקלטור וכהן גדול.
R’ Yochanan said: [G-d spoke] to the angel who was the most severe of them - This was Gavriel, as it says, “but one man among them was clothed in linen, with a scribe’s slate at his loins.” This angel served three functions: scribe, executioner, and High Priest.
How can these sources be reconciled? Can an angel have only one mission, or can he have three? If you want to argue that, for whatever reason, Gavriel is different, the Midrash in Bereishis Rabbah proceeds to detail which angels were involved and which task each one had:
מיכאל אמר בשורתו ונסתלק גבריאל נשתלח להפך את סדום ורפאל להציל את לוט.
Michael said his news [that Avraham would have a son] and left; Gavriel was sent to destroy Sedom; and Refael to save Lot.
But if Gavriel can perform multiple agencies, let him do all three! Are we forced to say that these Midrashim are in conflict, or is there a way of reconciling them?
(I see that the Anaf Yosef to Eichah Rabbah asks this question, leaving it unanswered. He’s referenced in note 69 in the Artscroll edition, and the piece in question is written out on the Hebrew side on page ד, for those who want to see him inside.)