First, you can render out your particles as Apple ProRes 4444 with an alpha channel for compositing in a separate application, like Adobe After Effects, Blackmagic Davinci Resolve, Final Cut Pro, or any other video editing or compositing application.
Second, you can import a Particle Illusion project from the standalone application into the paid plugin version, and finish the composite there.
You might also be able to create a large single particle that uses a version of your footage. This would be lower quality and useful for positioning the particle effects only – and could cause performance issues. Visit the Particle Illusion Forum for more information.