A method is provided for manufacturing a component. This method includes additively manufacturing a crucible for casting of the component. A metal material is directionally solidified within the crucible to form a metal single crystal material. A sacrificial core is removed to reveal a metal single crystal component with internal passageways. A component is provided for a gas turbine engine that includes a metal single crystal material component with internal passageways. The metal single crystal material component was additively manufactured of a metal material concurrently with a core that forms the internal passageways. The metal material was also remelted and directionally solidified.