All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
It is not a recommended act of Sunnah to pray voluntary prayers after the break of dawn, between the Athaan and Iqaamah, except for the confirmed Sunnah of Fajr. However, the scholars have differed in opinion regarding voluntary prayers that are performed for a specific reason, such as after ablution and upon entering the Masjid, in terms of whether it is permissible to pray them or not.
The view we adopt is that it is permissible to pray such prayers at that time, even though praying the two Sunnah Rak'ahs of Fajr suffice from having to pray these two prayers since they are not intended as independent prayers. A person is asked to perform a prayer after ablution, and to pray upon entering the mosque before he sits down. So, performing any other prescribed prayer, obligatory or recommended, is enough and substitutes these two prayers.
Allah Knows best.