Unless your water contains salt then a standard water softener of the correct size should remove all the mineral. Your iron filter- is it an air injection system? or does it use potassium permanganate? or is it an ozone system? They did install the iron filter before the softener correct?
After you get the iron and mineral out of the water you could then install a carbon filter to catch 'some' contaminants'. Or use a reverse-osmosis system only for drinking water.
After you get the iron and mineral out of the water you could then install a carbon filter to catch 'some' contaminants'. Or use a reverse-osmosis system only for drinking water.