How to improve Biophysical Processor results?

I am trying the Biophysical Processor for the first time in Sentinel-2 Level-2A product. I have noticed the results are very sensitive to illumination causing huge differences in mountains and areas with relieve. The results are underestimating FVC (Fraction of Vegetation Cover) where there is more sun light exposition.

I was wondering if I’m probably missing some previous steps to perform before running the Biophysical Processor. Currently I am just resampling and subsetting L2A product before running the tool.

Here is an example of the FVC output:

And an orthophoto of the same area:

From most illuminated to shady faces of the mountain the differences can easily go from 0.3 to 0.8 but the real coverages should be almost equal.
To take a closer look:

I think the values are low in general, but the sun/shade effect it is too big to make this product usable for me.

Is there anything that can be done?