Appending multiple providers to the same context

I am going to provide a written example as I feel it's easier to understand than putting loads of code. The idea is that I have 3 main components (+ the App.js), whose children are irrelevant - Header/Product/Description. The main flow is that the App.js has a bunch of states that I need to pass down to all the 3 children. That has been beautifully adressed by context. However now, in the product component, I not only use the context that was provided by the App component, I also want to append a local state to it so that the other 2 components can use it as well. Is this possible without doing another, entirely different context? I actually tried to put another provider in there and append it to the rest of the context object, however that has not worked out.