Is it permissible to offer more than two supererogatory rak'ahs before performing the Fajr prayer?

The Sunnah (definition) is not to perform supererogatory prayers after the second adhan (definition) of Fajr, for the Messenger of Allah, peace and blessings be upon him, said: "Let your present inform your absent ones that there is no prayer after Fajr except two rak'ahs." And Sa'id ibn al-Musayyib said to someone who prayed more than two rak'ahs after Fajr: "May Allah not punish you for prayer, but He will punish you for going against the Sunnah." Therefore, one should restrict oneself to the two rak'ahs of the Fajr Sunnah.