I have my default character input mapping, with Shift on as the sprint key. When adding a second context to the player when they pick up an item, I want Shift to also serve as another input on this new context, whilst also retaining it’s sprint ability from the initial. Right now, it seems to override it, removing the players ability to sprint. Is there something that can allow the same input to serve both functions?
Consume input is probably on.
Aside from that, you just need to have one input determine what function has to happen.
Are you needing to sprint, or are you needing to aim?
How can you possibly tell what the player wants? Are you a mind reader?
No?
Then you need different inputs.
Yes?
Well then read my mind for a solution? 
And to be crystal.
You probably need to have a completely different input/behaviour based on whatever situation - say shift is hold breath while aiming down sight for instance. Goes back to the first point.
One input determines what function to call based on variables.