Yes. If you want to remove additional contaminants as well as hardness minerals, you can install a whole house filtration system alongside your upflow softener. If you can afford a whole house reverse osmosis system, this is something to consider.
But RO isn't always necessary. If you just need to remove chlorine and associated chemicals, consider a carbon filtration system, like an upflow carbon filter. If you want to boost your water quality by removing iron, install an air injection filter. A reverse osmosis system tends to be quite excessive for whole-home use.