Armor Piercing and Converting to Physical

Does armor piercing affect damage that has already been converted once to physical? Ex: if I have the Octavius head and chest piece with a 100% armor piercing weapon, will 60% of my elemental damage get converted to pierce, with no physical damage remaining? I know that damage can’t be converted twice, but I’ve heard it said that armor piercing is a separate mechanic. I don’t have any items that convert damage to physical, or I’d test this myself.

Thanks.

All damage conversion happens at the same time so a damage type is not converted twice

Yes, any conversion can happen only one time. A damage, that was converted from another, cant be converted futher (to prevent “conversion loops”, etc).
So if you convert some elemental to physical, THAT portion of physical damage wont be converted further to pierce, nor to any other damage type.