This is how you might distance-blend at least:
Plug whatever into the a/b inputs of the LERP. In your case it could be the strength-value of the blur, and you can set a value at the nearest distance, a distinct value at the mid, etc, etc. The LERP is a ‘linear-interpolate’ it moves between the a and b inputs/values based on the alpha-input. Assum at 0-alpha you get 100% a and 0% b. At .5 alpha it will be a 50/50 mix, etc…
As you divide the scene-depth by your specified blend-distances you are generating a number from 0 to x, but saturate clamps this between 0 and 1 (the range we want). Feed that to the various daisy-chained LERPs and you can create multiple ‘steps’ and set values-per.
The buffer-value is added in as a negative number (vs subtract, add is technically faster and/or more-packable) so as to create a dead-zone around the player, or an area where the blending math won’t (effectively) start so alpha will always be 0. Think you want a clear area around the player before the fog-stuff sets in and you start blending with the background (or if not fog, whatever you use).
If you do it this way, you can keep just the one blur-function and just feed it various values over distance, time, whatever you tend to use. More efficient.
Hope this helps.