When I make a multi-stage design, it typically grows as I go. But that means that the blueprint changes dimensions. So as I scroll through the generated book, the center that the mouse is pointing to changes between BPs. Is there an easy way to align BPs between stages, so that they don't jump about relative to the mouse? Is there some voodoo I need to set in the grid settings, either on default, or on individual stages?

Yes you can, using relative snap-to-grid.
Snap-to-grid, relative, and set the grid size to something like 2x2. Then, a flag appears that you can adjust with shift click, to where you want the cursor to be when placing the blueprint. The mod will make sure the blueprints align.

You can set this in defaults, or per-stage if you want to move the center around.

You can also set the grid to a larger size, with snap to grid absolute; this makes the blueprint a bit easier to align

Factorio by default uses the center of the blueprint as the cursor position; using relative lets you pick the position instead.

Thanks :) I'll have a play. I was using relative and couldn't find a way to make it work, but I'll give absolute a try. The kludge I was trying was including concrete tiles at the corners of the final bp size.