If a person is convicted of multiple counts of second-degree murder, can he or she get the death penalty?

All I know for criminal justice cases is that in some states if one person is found guilty and convicted of one or more counts of first-degree murder that individual would either be sentenced to life or get the death penalty for the crime(s). But what if one person is found guilty and convicted of multiple counts of murder in the second-degree, can the courts still give him or her the death penalty on that degree of the crime? I mean first degree means the crime is proven to be premeditated, deliberate, with malice. But second-degree murder is conisdered not to be premeditated but would be deliberate; therefore known to be a crime of pion. Which is acted out in heat of the moment without thought or plan of how to commit the offense.