Does such a preamp exist?

Check out Manley labs. I believe this is what your looking for.

I don't know if they are available balanced but perhaps the Silver Rock might work for you.

Investigate at www.dact.com, splendid attenuators in balanced mode.

The site is worth a visit for didactical reasons too.
Cheers

The Jeff Rowland Synergy preamps are balanced and have selective gain. Good luck.

The Pass Labs Aleph P has variable gain and balanced inputs and outputs.

The Levinson preamps like my 380S only apply gain when it is called for (about 19dB) based on the volume control position - from unity on down, the circuit actively buffers the inputs and outputs but applies no gain, and the sound does benefit. From what I've read, the forthcoming 320S will feature user-selectable gain including a 0 gain setting. All Levinson preamps of course are fully balanced with XLR I/O.

For you information, unless you have an odd unit, your pre amp does have a gain control with a subtractive position(s), a unity gain position, and a amplified position(s). On my preamp, using an amp with a 1.5v input sensitivity, about 10 o'clock is unity gain for 1 source and 12 o'clock is unity gain for another.

What you need to do is to reduce the output gain by using in-line attenuators at the amp, say 12db, or see if your preamp mfg can reduce the output gain. What kind of pre-amp do you have?

What is your pre, amp(s) speakers. And how big is your room? Maybe the problem isn't the pre. To me your question reminds me of someone calling their dentist, and telling them they have tooth that hurts. Of course the dentist canoot tell them what is wrong without examing :)

I am not familiar with this product, but it does look promising.

http://www.bentaudio.com/index2.html