don't have two synths playing in the same octave (at the same time)
Wait what?
I suppose you mean the combined synthsound that may consist out of several synthlayers (many within the save octave) to make a fuller sound.
It may be a bit true if you have one synthsound playing and another one within the same octave at the same time, but this shouldn't be any problem if you have good mixing habits. It also has to do a lot about the sounddesign features and timbre as well. Some may work perfectly playing together due to the right designing, while some just collide and requires a bunch of mixing to separate them.
Anyway, to answer the OP, if you think your mix sounds dull, but gets aggressive when you boost the highs on the EQ, then it may be because the highend has a lot of dynamic range, meaning there's a lot of space between the average volume and the peaks/strums.
Then it's all about reducing those dynamics before boosting it to simply make the smooth average volume-floor a bit louder without boosting the peaks and strums.
Simply pull up a multiband compressor, and dial in peak compression in the high range, and gain compensate. Then you can do the EQ boost on the highend, and it should sound a little more bright yet controlled.
Note that overdoing this may result in a pumping and overcompressed highend, which won't sound good at all.
However, good mixing habits is also key. Some frequncies may mask other ones of they're too apparent, making only the loud peaks and strums of those otherwise masked frequencies be audible. Then when you boost the highs, the peaks are still the only ones that increases in perceived loudness, making it only more aggressive and harsh.
For instance, a sound may be too boxy/muddy, masking the highend. A newer producer would probably cut the mid a bit, and then boost the highs - but never quite getting there. Instead, cut only the mid - a lot and GAIN COMPENSATE, and then take it from there. Suddenly it may be all nice and clear because the volume floor in the highend isn't masked anymore.
Though, all of these tips are pointless if the sounds doesn't have any highend from the start. The sounds themselves needs to be designed well.
This involves adding noise to a sound, or adding a highpitched oscillator to give it some sparkle, or using samplereduction/sample&hold, or even using real bitcrush.
And of course layering is a very powerful option, you can even layer percussion and such to create highend, etc.
The problem with using distortion to brighten sounds is that distortion often give a harsh and overdriven sound where all frequencies affect eachother, at least if you use it badly. In my opinion, using distortion for brightness is better if you want to extend the brightness in for instance a decaying sound, rather than increasing it. Saturation may be a bit better, but it doesn't increase that much, and you're left with a sound that is still too dull.
One better choice for distortion though is using parallell distortion or multiband distortion. You could for instance create a send, highpass the sound a bit making it thinner, then distort it, and then highpass it again, then blend it in, and the distortion may "behave better". Though you may need to correct the new frequencies a bit with EQ.
And then we have the good ol' iZotope Ozone multiband saturation and other plugins that adds content without harming the timbre too much.
Here's a video which hopefully will help you out... At around 4:38 or so he talks about the usage of multiband compressors for evening out the highend
