Dual management structure

Dual management structure

I was informed this week that because another department in our company is swamped and needs more help, I will have to take on more responsibilities for them and will now have two managers moving forward. The team I’m already on is also short-staffed, and all of us have absorbed more duties after employees have resigned or been let go, with very few new hires in the past few years. I already do have a full schedule and have no idea where I’m going to find time to do even more work. I also don’t know what the work will entail yet.

How should I approach this to ensure that my job responsibilities don’t become too overwhelming? How have others in this situation handled prioritizing responsibilities from two separate departments? I want to ask for a raise to reflect the increased workload and additional responsibilities but expect this to be met with resistance from higher up, as they don’t even give us cost-of-living raises every year.

I have started looking for another job, but in the meantime I need to make this situation tenable. Any advice would be appreciated.