CEP/Audition has an option to apply fixed or faded volume: Effects | Amplitude | Amplify/Fade. Both tabs allow you to modify the L and R channels independently, if you wish. The Constant Amplification tab raises the whole highlighted selection -- you guessed it -- by a constant value. The Fade tab allows you to highlight a section, apply a starting amplification (positive or negative) and an ending amplification, and then determine how to transition from the starting amplification to the ending amplification (linear or logarithmic). This might accomplish what you need.
Alternatively, if you need greater / more complex amplitude control, CEP/Audition also has two envelope tools, one in Waveform view (Effects | Amplitude | Amplify/Fade), one in Multitrack view (just click the horizontal line near the top of the waveform to create your envelope points). I never cared for the envelope in Waveform view, and never used the one much in Multrack view (as I moved to a different editor), but they're there and you might find them useful.