Double Damage Conversion?

I was thinking of a build with the Infernal Mantle (25% fire dmg converted to Chaos dmg).

I looked over for information regarding double conversion and such and I don't seem to be able to find that information. Most posts are for phys / elemental conversions and in the case where there are only two types, only 1 conversion can occur.

So my question goes as follows:
If I use the Burning Arrow gem, which converts 50% of phys to fire, with a Blackgleam(30-50% phys to fire), I would end up with let's say(to make it simple) 100% phys to fire.
Now if I wear an Infernal Mantle, which converts 25% of fire damage to Chaos damage, would the conversion apply to the converted total of fire damage?

yup you'll end up with 75% fire 25% chaos

Are you sure about that, because one TYPE of damage can only be scaled to 100%, and we do not go over 100% in physcal conversion. We convert 100% of phys in Fire then 25% of fire into Chaos.