I know that after the salaat of fajr and asr one cannot pray nafl salaat but can one pray qada salaat at these times.
As Salaam Alaikum.
It is permissible to perform Qadha Salaat at these times. However, you will need to stop its performance when the sun is rising and when it is setting. ( Kitabul Fatawa Vol.2 Pg.1128 Zam Zam publisher Karachi 2007).
And Allah Knows best
Mufti Waseem Khan.