Is it permissible to supplicate after Al-Fatiḥah or recite a short surah from the Qur’an in the third or fourth rakʿah?

The places for supplication in prayer are well-known, and what comes after Al-Fatihah is not among them. What is legislated after Al-Fatihah is the recitation of a Surah or whatever is easy from the Qur’an, or bowing in cases where Al-Fatihah alone suffices, such as the last two Rak’ahs of the four-Rak’ah prayers. The prophetic Hadiths indicate that the Prophet, peace and blessings be upon him, would limit himself to Al-Fatihah in the last two Rak’ahs of Dhuhr and Asr prayers.