Remove a stroke at intersections
I have some lines with a stroke to give it width, then another stroke to outline that.

My goal is to get rid of the outline stroke at places the lines are intersecting (example made in Ps)
Current:

Desired output:

I know I could kind of do this if I converted my lines to use a fill and stroke but I'd prefer to keep them lines if possible.
Any ideas how to do this? Is it possible without just using fills/strokes and using the shape builder? Thanks in advance! 🙂

