*argue (something) out*
Definition: to discuss an idea or plan in detail, covering all the aspects and possible consequences, in order to reach a decision.
E.g.1: It’s an interesting proposal, but I’d like to argue it out with you before agreeing to it.
E.g.2: While they were arguing out the plan they realised that it would cost too much money.
This phrasal verb can be separated. (E.g.1)