"The first thing I would do is ask my team to stay focused on their current work while I make an impact assessment given the current variables. I would determine which resources would be needed for the new request and how much time would be required to complete it. Then, I would work to determine a list of viable solution options. This might include things like asking other teams if they have resources to spare to help us complete both deliverables, talking to both of the clients to see if they could absorb a delay, or talking to the team to see if anyone has bandwidth to take on the extra work.
I would then discuss the results of my analysis with my senior management and work with them to determine the best way forward for the clients involved. Ultimately, I would strive for a plan that honors the original commitment and delivers the new request as quickly as possible without burning out my team."