Is it permissible to pray the sunnah (recommended prayer) that precedes the obligatory prayer after the time for the (obligatory) prayer has elapsed?

A Muslim must perform the prayers at their prescribed times and in congregation if possible. It is not permissible to delay them without a valid excuse. If it is 2 o'clock before the entry of 'Asr time, then the Dhuhr time is still ongoing, and performing its pre-prayer regular Sunnah is permissible. However, if 'Asr time begins at 2 o'clock, then according to some scholars, the Dhuhr time has expired, and performing its pre-prayer regular Sunnah would then be a permissible make-up prayer.