Update: I got it wrong. You have to make actual copies of the files to the folder. It won't open multiple shortcuts. Alas.

I've come up with a work-around for this. I create a folder called "Working Documents" and put shortcuts to the relevant files in it. In Windows Explorer, you can highlight multiple files in a folder, press enter, and all of the files start up at once! It's kinda annoying that you have to create a dedicated folder for it, but it works.