Does the prohibition of prayer after the Fajr prayer and the 'Asr prayer include all prayers, or are there exceptions?

The Messenger of Allah, peace and blessings be upon him, prohibited prayer after Fajr prayer until the sun rises, and after Asr prayer until the sun sets. This prohibition is general and includes all prayers, except for certain prayers that have been exempted by text or consensus, which are: repeating the congregational prayer, the two rak'ahs of circumambulation (Tawaf), salutation of the mosque (Tahiyat al-Masjid) upon entering the mosque on Friday while the Imam is delivering the sermon, salutation of the mosque upon entering the mosque after Fajr or Asr, the solar eclipse prayer, the two rak'ahs after ablution (Wudu), and the Istikhara prayer if the matter cannot be delayed. The summary is that the prohibition does not include prayers with a specific reason.