How can I connect one DB to multiple vercel projects?

Neon seems to impose a 1-1 mapping between vercel projects and neon DBs. How can I connect one DB to multiple vercel projects? We have one database but 3x projects in Vercel that all need to use it for preview branches and production. As soon as I connect one project, it disconnects another. You need a vercel integration like sentry does that lets you specify each vercel -> neon pairing. This single connection only is very prohibitive. How can I fix without migrating to Vercel postgres?