What is the ruling on supererogatory prayers that are not prescribed [in Islamic law], such as praying four rak'ahs after 'Asr, Maghrib, or Fajr prayers?

Initiating a supererogatory (nafilah) prayer after the obligatory dawn (Fajr) and afternoon (Asr) prayers is prohibited according to many scholars, with the exception of supererogatory prayers that have a specific reason. Some scholars disliked performing supererogatory prayers after these two, except during the precise times of sunrise and sunset, when it is absolutely forbidden. As for supererogatory prayers after the Maghrib (sunset) prayer, they are permissible; in fact, they are encouraged between Maghrib and Isha (night) prayers, and are considered part of the night vigil (qiyam al-layl).