It is not permissible. Ata' and al-Nakha'i disliked it due to its resemblance to the speech of humans, and because it is a supplication for a specific person, so it is not permitted, similar to responding to a sneezer (tashmit al-'atis). The prohibition of responding to a sneezer has been indicated by the hadith of Mu'awiyah ibn al-Hakam al-Sulami (24).
Section: It is recommended for one praying a voluntary (nafilah) prayer that when they pass by a verse of mercy, they should ask for it, or [if they pass by] a verse of punishment, they should seek refuge from it. This is due to what Hudhayfah narrated, that he prayed with the Prophet (peace and blessings of Allah be upon him), and he would say in his bowing: "Glory be to my Lord, the Almighty," and in his prostration: "Glory be to my Lord, the Most High." He did not pass by a verse of mercy but that he stopped at it and asked, and he did not pass by a verse of punishment but that he stopped at it and sought refuge (25). It was narrated by Abu Dawud (26). It is also narrated from 'Awf ibn Malik, who said: "I stood with the Messenger of Allah (peace and blessings of Allah be upon him) one night, and he stood and recited Surat al-Baqarah. He would not pass by a verse of mercy but that he would stop and ask, and he would not pass by a verse of punishment but that he would stop and seek refuge." He said: "Then he bowed for a duration similar to his standing, saying in his bowing: 'Glory be to the Possessor of Might, the Dominion, the Majesty, and the Greatness.'" It was narrated by Abu Dawud (27). It is not recommended...
(24) He said: 'While I was praying with the Messenger of Allah (peace and blessings of Allah be upon him), a man from the people sneezed, so I said, "May Allah have mercy on you." The people glared at me, so I said, "Woe to my mother, why are you looking at me!" They began to strike their thighs with their hands. When I saw them trying to quiet me, I remained silent. When the Messenger of Allah (peace and blessings of Allah be upon him) finished praying—and may my father and mother be sacrificed for him, I have not seen a teacher before or after him better in teaching than him—by Allah, he did not rebuke me, strike me, or insult me. He said, "This prayer of ours is not for anything of human speech..." etc. The hadith was mentioned previously on page 236.' (25) In the original: "and he sought refuge" (wa ta'awwadha). (26) In: The Chapter on what a man says in his bowing and prostration, from the Book of Prayer. Sunan Abi Dawud 1/201. It was also extracted by al-Tirmidhi in: The Chapter on what has come regarding glorification (tasbih) in bowing and prostration, from the Chapters on Prayer. 'Aridat al-Ahwadhi 2/63, 64. Also by al-Nasa'i in: The Chapter on the reader seeking refuge when passing by a verse of punishment, and The Chapter on the reader asking when passing by a verse of mercy, from the Book of Opening the Prayer; and in the chapters on dhikr in bowing, another type (of supplication in prostration), and supplication between the two prostrations, from the Book of Tatbiq. Al-Mujtaba 2/137, 149, 177, 178, 183. Also by Ibn Majah in: The Chapter on what has come regarding recitation in night prayer, from the Book of Establishing Prayer. Sunan Ibn Majah 1/429. Also by al-Darimi in: The Chapter on what is said in bowing, from the Book of Prayer. Sunan al-Darimi 1/299. And Imam Ahmad in: Al-Musnad 5/382, 384, 388, 397. (27) In the previous chapter, and the previous location.