"I love a good challenge, but I have to admit that this sounds like a handful. I will talk to my superior to find out if I'm the only option at the moment. If there are other project managers available, then I would probably ask them to start the project and then I can take over once my bandwidth allows it.
If I'm the only option then I have to set realistic expectations with my manager. For example, I can work out a schedule for the new project that starts out loose and progressively tightens as I close out my other ones. I can then leverage resources that are available to me. One way I can do this is by gradually delegating certain tasks to stakeholders or team members. The two current projects should already have an established cadence, so I'll do my best to manage progress at a higher level. Another resource I can leverage is automation, such as project management software. I will automate task follow-ups so that I don't have to spend too much time getting updates from team members."