If you want to use drink mix in the bottle, just unscrew the spout and remove the filter temporarily. Problem solved. Of course, if the point is to filter the water *AND* use the pre-filtered water to make a powdered drink, then the best thing is to carry an extra plain drinking bottle; squirt from the Brita into it, and you'll have filtered water to mix your drink.
I have other filtered bottles, but they don't accept ice as easily as the Britas. BTW, if you can't find them in stores anymore, they can be found on EBay.