Can a causative have an indirect object? For example: I made my friends give me a new phone?
Me there is the indirect object of give, not of the causative make.
Catenating causatives like make, let, have don't really take "objects"—they take clausal complements. Pronominal subjects of infinitival complement clauses are often cast in "object" case—transformational grammars call this "raising to object"—but they are only morphologically objective, objects-by-position rather than objects-in-fact.