Can the judge prescribe a Ta‘zeer (discretionary punishment) that exceeds the Hadd (prescribed corporal punishment) in some crimes that entails Hadd or Qasaas (retribution)?

All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

Ta‘zeer is a discretionary punishment imposed by the Muslim ruler or judge for a crime or sin for which the Sharee'ah has not fixed a specific punishment; or, it has actually fixed a punishment for it, but the conditions of carrying it out are not fulfilled. As for the Hadd, it is the corporal punishment determined by the Sharee'ah for the interest of the group and for protecting the public system, which is the greatest aim of Islam. This Sharee'ah-prescribed punishment cannot be dropped by an individual or a group. If (obtaining general) interest (for people) entails applying Ta‘zeer to the one who committed a crime, then there is nothing wrong with that. This did happen at the time of ‘Umar, when he lashed the one who drank alcohol eighty times, adding 40 lashes to what the Messenger of Allah and Abu Bakr did—lashing the one who drank alcohol forty times only. Also, a man who had drunk alcohol during the daytime of Ramadan was brought to ‘Ali ibn Abu Taalib and he lashed him eighty times as a prescribed punishment and an additional twenty for breaking the fast in Ramadan. [Imam Ahmad]

Allah knows best.