I've had that probelm a couple of cars ago.
The sub amp draws a lot of current and that will pull down your voltage, so your amp for the highs will clip sooner.

I know i'll get a lot of flak here for saying so, but a big cap will solve that problem.

Like I said, that was 2 cars ago when i had a total of 1000 wrms.
I put in a 1 F cap and the clipping and lights dimming went away.
My last car had 1500 wrms so i went up to 2 F. It worked.
In my new car, which came with a 145 amp alt, big battery and larger wire all around, I'm running a total of 2020 wrms and using a 1 F and a 2 F cap.