Your team is already busy with a lot of things when the next project lands on your desk. Can you give your people more to work on? Yes, you should! You’re not responsible to manage their time, you deal with grown-up professionals. Delegate all you have. But, make clear at the same time that you don’t want to overwork them. They can come with suggestions for activities that should be delayed or dropped if there is too much on their plate. The minute that you decide to take off less important work, your team will know that you care about them.
You’re under pressure because you definitely started this important project too late. How