Alexandria -- multiple bibliographies in the same document!

Of course!

The main thing I wanted was for the bibliography to not show up as a separate chapter, as it belongs to the previous chapter, which I fixed by naming all of the various chapter bibliographies “Bibliography” and then set the following show rule:

show heading: it => {
    let levels = counter(heading).at(it.location())
    if it.level == 1 {
        if it.body == [Bibliography] {
            set align(center)
            text(it.body + " For Chapter " + str(counter(heading).get().first() - 1), fill: header_colour) 
            counter(heading).update(counter(heading).get().first() - 1)
        }
    }
}

This essentially just means that the smaller, non-numbered header for the bibliography will read: “Bibliography for Chapter [insert chapter number]”

Hope this is what you were looking for.