>> It's great if there's actually stuff you can turn down, but more often than not there really are business objectives that won't be met if you don't do the work.

Make it about resource planning. Two stories:

One of my old managers was really good at getting himself in meetings where new business was being discussed. Even if he wasn't invited because people didn't think our team would need to be involved in a project. He could either convince them that we didn't have resources, we needed additional resources, or we could make due (maybe shuffle a bit) with what we had. Our team was almost never blindsided.

I was running a small software team doing multiple embedded projects. We had more projects than people, but I made a chart breaking software for each project into common high level components (some were N/A of course, some were largely reusable) and showing percent complete on each one. In one meeting I simply showed that one of the smaller projects had zero percent completes across most components, and said it was going to stay that way for the foreseeable future due to all the other partial completes on higher priority products. That one got cancelled within days.

I've come to appreciate an important part of management is to prevent these interruptions from reaching the people doing actual work, or to... you know "manage" the workload on behalf of the team.