Step-siblings are children born of two different families who have been joined by marriage, defacto or otherwise, of at least one of their respective parents. A male step-sibling is a stepbrother and a female is a stepsister.
English has no name for a step-sister's half-brother but try drawing the relationships in diagrammatic form, rather then describing them in words. If English was.
and Joe get married, Alexis and Brandon would be stepbrother and stepsister. Sarah is a half sister to Alexis, since they share the same mother but not the.