Would increasing the gain in the amp give more weight to the sound? Any negatives?

In integrated amps with passive preamp section it's common not to have full body sound, but transparent. I heard Creek amps with passive section and described them as Brittish-polite and shy amps. I like'm somewhat rude and brave -- in other words completely opposite.
It's not good idea to increase gain of power amp. In most cases the amp can loose stability and become microphonic, pick up emi and simply self-oscillate and hum. 
So theoretically and most trivial, you probably need active preamp and use your integrated as poweramp only.

All you need to do is to move your volume control all the way up and use one of line inputs of your integrated with preamp of your choice. Otherwise to move the right way you simply need to go to separates from your integrated amp.

well musical fidelity has inexpensive unity gain buffer device that also inverts the phase. one can be placed between the source and amp, but active preamp will work much more efficient than even mentioned inverting transformer. I struggled when I had Creek 5350 SE integrated amp till I purchased active preamp Classe 30. This preamp turned polite and shy Brittish amp into substantially better version...

erik_squires804 posts09-22-2016 1:58pmGain does not affect body. 

In reality gain (in pounds :-) directly and surely affects body. To test it, switch to ice cream, apple danish with coca cola few times per day or more and drive-thru adventures via famous American food chains to experiment on body and gain.

Aside from humor, gain is important to reach necessary signal strength. If it's insufficient, than there will be an insufficient body. Gain must be increased either at source or preamp level. Gain of poweramp will affect the output power, but if there's not enough input signal, this gain obviously won't affect body or even if it will it may not be to the benefit of sound quality.