Common content across network

I’m setting up a network of four sites for a client. They’re going to have content that is common to all sites (history, philosophy of care, directions, and the like). I’d like to give them a way to publish this stuff once, as pages, in the main site, and have that content pulled through to pages on the subsites. I can put together a shortcode that pulls content from one post and drop into another post or page, but I don’t know how to do that on a network because while I can query by post ID, I don’t know how to query posts in a different table. Can this even be done?