Differently weighted bevels for subdivision surface?

I really like the idea of using a bevel modifier as a non-destructive means of adding supporting geometry before a subdivision surface modifier. Here are the settings I am currently using. The highlighted portions are the essential ones:

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And this works quite well, but with a one big problem that I’m hoping to find a solution to. That problem is, what happens when two bevels of different weights intersect.

You get this weird kind of pinching, where the narrower bevel overrides the wider bevel. Is there any way to achieve my desired result with the current bevel modifier? Because having to manually correct the results rather defeats the point of a non-destructive approach.

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Did you hit Ctrl + A and apply all transformations first?

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Yes, this isn’t an issue of unapplied scales or anything like that. It is an issue of how the bevel modifier handles scenarios where you have differently weighted edges intersecting.

Perhaps I should have stuck with a cube as a simpler example:

Here is how I have applied different bevel weights to the edges of the cube. On the left I have two wide bevels intersecting a narrow bevel, and on the right I have two narrow bevels intersecting a wide bevel.

Here are the results of the applied bevel modifier above, and the result I am attempting to achieve below:

Essentially, where narrow and wide bevels intersect, the bevel modifier prioritizes the narrow bevels at the expense of the wide bevels, and I would rather it did this the other way around:

The reason this matters is because prioritizing the wide bevels produces a drastically better subdivision surface result. With the current bevel modifier, wider bevels appear to bend inwards where they intersect narrower bevels.

The best description of good bevel modeling I have seen is from a youtube channel called blenderbob its not non destructive but blenders bevel modifier is not ideal for more complicated bevels.

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