This is not an easy one to answer. Let me break it down into general terms--which may or may not be applicable to your system--it's almost impossible to know.
Brightness can be caused by a variety of things, the problem is that not all of those things are bad. Sometimes brightness is a result of having a higher resolution system. Sometimes a prior component may have actually been "dull", or rolled off in the frequency extremes. Then you upgrade, to find a sound that is not as pleasing. This of course ties into system synergy, but I'm going to turn this response into an area that I know very well--acoustics.
Acoustics play a huge roll in the overall sound of a system, bright or bloated in the bass, most of the problems come from the room interaction. It is possible you did improve the quality of your components only to discover shortcomings in the room--not really that surprising--it happens all the time. Unfortunately, many people will say use "xyz" interconnects to tame the high frequency, or "abc" power cord to mellow the sound. These things do make a difference, but I don't think they should be tone controls.
On the other hand, there is quite a lot of equipment that is very good, but some lean towards the lean sound. That's okay, but if you have 3 pieces of equipment that lean towards the lean and bright sound--well, you can figure out what the result will be. This is an important part about system synergy. In the perfect world, everything we would be neutral, but we know that isn't true.
Now, I'll go back to the room issue. Have you measured the room response? This can be done easily and cheaply (it can be done expensively too--but you can start with a basic test CD and meter and get some reasonable results). This will just let you know if the frequency response is relatively flat. You may need to add some absorption to get a flatter response. Absorption at the first reflection points is generally a good idea to tame the brightness.
If you haven't already evalutated the room and some basic acoustics, I would start here. It will make all the changes down the road far more meaningful.