Is it possible to have a curve object with both "taper object" and manual width adjustment?

I need to have many short curves, and I would like to control their overall shape with a taper object while individually adjusting their widths. If there’s no taper object I can adjust the radius of individual points, but the taper object overwrites that rather than working together. I would like to keep the curves as a single object to avoid unneeded extra work if I have to adjust their other settings and modifiers.

This image shows a simplified setup, but the actual project is much more complex with many more curves.

Does setting the taper radius to “multiply” help?

That’s exactly what I needed. Looks like it’s a newish feature, updating my blender made it appear.