Set and hold your boundaries
"My team and I would be happy to take this important project on, but we are focused on a couple of other priority work streams. We won't be able to help over the next month or so. Happy to brainstorm with you alternative solutions."
Sooner or later you're going to have to say no to lower priority project requests.
If you're not ready to say no, you can say it indirectly. This helps open up the conversation about prioritization and alternative solutions, while easing the negative blow.
Here is an example of a soft indirect no:
"I can scale back what I can give you by the end of the week, or complete the project by next week. Which works better?"
When you set boundaries in a collaborative way, you are upholding your commitment to your priority projects.
Also, you establish a leadership brand that speaks volumes about your clarity and commitment.