There's a provision in the TPP (which is this 'unrelated trade bill' you speak of) that allows for extension of 215 of the USA PATRIOT Act. It's not a filibuster; but it's definitely related to the TPP.
Page-by-page of a single bill doesn't work, though; see also attempts at a "line-item veto". For the most obvious failure mode, consider a bill that replaces one tax with another and a veto on the removal of the old tax. Or consider a bill that adds a tax and a service funded by that tax, and a veto on the service but not the tax.
It's a fuzzy ideal that you can try to stay close to, but it can't be a point of procedure because it has no actual definition.