In reality, Pat's project portfolio looks like Figure 3.
Once Pat has a picture of all the work in her group, she can have a conversation about which work to staff and which work to say no to. And, she can build a more realistic picture of the overall project portfolio with her peers so their boss can see what they are really doing.
When Pat shows her manager her portfolio, he says, "I had no idea you were working on all those projects. What's this business with support?" Now, they can have a conversation about all the work she and her team are trying to complete.
After discussing her current portfolio with her manager, Pat decides to tackle the "no" problem. "What would you say if I said no to more work?"
"Well, I'd think you were turning me down for a good reason. I'd probably want to see how people are allocated, to make sure everyone is working on the most important work. But I wouldn't fire you over a no."
Now, Pat and her manager meet biweekly to discuss how everyone is assigned to projects and for how long. Everyone is working on just one project during a week, and people are taking turns on the support work. She's also queued up the support work so team members don't have to interrupt what they are doing to manage it.
No is not easy to say in the organization, but it is necessary. Try showing your manager your work and explaining when you can get to new work. You are being a team player, you're not a slacker, you don't have to feel guilty, and you are certainly not letting anyone down.
You may be pleasantly surprised to have your well-defended no accepted.