Is it permissible for me to supplicate for Muslim men and women after the second Tashahhud in every prayer, using supplications from the Holy Quran and elsewhere?

It is permissible to supplicate during prayer for the aforementioned individuals, based on the Hadith of Abu Hurairah, may Allah be pleased with him, that the Prophet, may Allah's prayers and peace be upon him, used to supplicate for men he named after rising from bowing, saying: "O Allah, save Al-Walid ibn Al-Walid, Salamah ibn Hisham, Abbas ibn Abi Rabi'ah, and the oppressed among the believers. O Allah, intensify Your grip on Mudar and make it for them like the years of Yusuf."