It's one thing to deal with one manager. It's worse dealing with another. And another. And all those stakeholders who think they can have a piece of your time to do work for them. Not only can it drive you crazy, but you can end up getting a poor performance review from too many bosses and too little time.
All is not lost in this situation, though.
Your task management system is what you use to keep track of what you need to do and when you need to do it. You might think this is just a 'to-do' list, but a system is more than one part. Your calendar is one part of your task management system. So are your reference files. And so is your to-do list.
When it comes to having too many bosses, your task management system is critical for a particular reason: it is the complete inventory of the work you need to do and when you need to get it done. Without the inventory, all your talk about "too much to do" isn't very clear to anyone on the outside looking in. Your inventory of work is what shows others how much you have to do. Only then can you have a discussion on what the priorities are for your work -- and what you don't have to do.
Let's be clear here: your manager is your most important customer. Not your customers, not your stakeholders, not your teammates, not your coworkers, no. Your manager is your most important customer. Your manager writes your review. Your manager hired you (or inherited you) to help reach your manager's goals. Your manager can push back against outsiders asking you to do work and can re-prioritize your work with others.
Fail your manager and it doesn't matter how many people you have asking for your time; you'll fail.
(And, of course, the huge range of effectiveness managers have in helping you here makes a difference).
If you have your inventory of work and your manager comes first, the rest is prioritizing by managers. Your manager has first dibs on your time and effort. Point out the inventory, point out the conflicts and ask your manager to help with what you should be working on to meet his or her business goals. And, by the way, if your manager starts you working on something that is not in your goals, then you need to talk about the impact this work will have on meeting your goals.
But, let's just say your manager sucks and does a lousy job at pushing back on the workload and doesn't want to engage others about prioritizing work. Now you'll have to point out your priorities and workload to other managers who ask you to do work. While keeping focus on your manager's goals and knowing your inventory of work, others will get that you are working overtime to get stuff done and will (usually) move stuff around for you.
Without having your own house in order, though, all that push-back will be for nothing.
How do you keep track of all the work you do? How do you handle this situation?