How to keep objects separate when exporting SVG from Blender with the Freestyle SVG Exporter

Let's say I have 3 objects in Blender that I want to export to SVG.

In the SVG, all the lines are merged in the same group. Is there a way to have them grouped by their corresponding objects ?

Basically, I would like to be able to have independent groups for each Blender object in the SVG, so that when I move one, I could reveal the hidden face from the back object.

Using Blender 3.1.2

Blender view:

3 objects in blender

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