STAAD.pro has some composite design capabilities, but only limited codes are supported. Check the program help contents - index - composite to see the documentation.
Meanwhile, for a mid-rise composite structure we would typically advise users to use Ram Structural System which offers intuitive and robust composite beam design. We offer something called the Structural Enterprise License (SEL) for those users who might want to use RAM on one project and STAAD on another without having to purchase both packages outright. Let us know what design code you need so we can make the best recommendation.