Instead of saying you don’t have the bandwidth to do something, tell Execs what your team is working on, and the impact of taking up the new work on timelines of current projects. Help them do the trade off.
You will come out as thoughtful vs someone who can’t get things done.
This took me years to learn. Earlier I would focus on how to say the No than show them the trade off that needs to be made. And that never worked.
More gyaan on communication and how to run projects better: How to communicate better