Everything I've read about water filters on the tap (PUR or BRITA) says that it's not a great idea.
I've read that these filters remove trace elements that your fish need/like.
I'm not an expert on it, but I know I've NEVER read about anyone recommending it; but I have read several times that it's not a good thing.
Personally, I don't think you can do much better than what you are doing right now. Having said that... I also believe in backup systems. If you ever have a failure with your main filter (burnout of a motor for example) its good to have another filter running to hold things together until you can get it fixed.
I know in my city there are only 1 or two LFS's I like to support financially. If I had a failure on a Saturday evening, I'd be in trouble until Monday morning because they are closed Sunday's. Even if they were open Sunday's, they aren't open Saturday Night and my fish would likely be dead by morning with no filtration (at they very least, they'd be very stressed).
Therefore, I run a Fluval FX5 and a Fluval 404 on my 180 Gallon. IF the FX5 ever went down, the 404 would at least provide some filtration, and I could move the biomax from the FX5 into a media bag and hang it in front of the 404 output in the tank to keep the bacteria alive.
(Jeeze, that's a long answer) Anyway, I think it's a MUST to have a second filter, but I don't think your going to improve the water properties much.
Take Care.
Undey