I've found it to be the case every time. The reason some full range speaker systems have multiple tweeters in the design is to compensate for the more pronounced bass output they have. I had a very bass heavy, dark sounding speaker system once that had 5 (count 'em) 5 tweeters and two midrange drivers per side. Why. Because the 3 12" speakers per side would bury the highs. 5 tweeters per side and they still were dark sounding and darker than I personally prefer.
What we hear from a speaker system is the mix of all the frequencies they produce. Any speaker system will become brighter as we reduce the bass output or darker as we reduce the treble. Think back on the days when preamps had tone controls.
I know of no good speakers that use multiple moving coil tweeters. It is not necessary and the comb filtering response anomalies will be severe.
But Joe Schmoe is 100% correct you can not correct a bright speaker with a sub. Here is how to prove it.
If you have a bright speaker playing a Bach violin sonata it is excruciating. Turn up the sub all you want. No sound from the sub, still excruciating.
Now the original poster was concerned about sibilance. Now that is always associated with response anomalies centered around 5 KHz, usually from 4 to 6 KHz. You won't cure that with a sub. On some sources you might mask it to the untrained ear. The trained ear will find it right away. The most important feature of a speaker is that it have a smooth response from 200 Hz to 10 KHz at least with a good spl. If it deviates in that range more than 3db it is a poor speaker, and that takes care of most. To be considered as possibly excellent it must be within 2 db. The off axis response must mirror the smooth axis response. A quality deep bass is a luxury. It is the extended midband that has to be right first. Then there are a host of other problems that have to be taken care of before excellence is achieved. However without a smooth midband on and off axis a speaker does not get past the starting gate.
Now I have been at this a long time. I have never found Eq useful for anything except touching up a vintage recording. If you are reaching for Eq with a good deal of program material, let alone leave it in permanently, it is time to look at the speaker, find and correct the problems.
Most of us are not playing our equipment in the corridor or public toilets. Good speakers interact with their environments and produce a believable pleasant sound stage in a wide variety of environments. The problem is 99% of speakers fall way way short.
Now I'll grant that an ambient environment will detract some from pop and jazz etc. But for classical music good speakers will interact well with a somewhat ambient space when reproducing most classical recordings.
My main listening room is to my taste slightly on the dead side, despite the fact that I increased window areas etc. I would not want to reduce any reflections at all. However for movies it seems very good, so on balance I'm happy. I'm very impressed how Dolby PL IIx music really does realistically restore the ambiance of the recording venue, on fine recordings.
So My advice to the original questioner still stands. Turn off the the crapo, set everything flat and see how it sounds for a week or two.
