The only way to adjust the individual volumes and other voice parameters of the Main Voice, Dual Voice, and Split Voice is to go into the Function menu, scroll until you find the specific voice parameters you want to adjust, and then change their settings as desired. See pages 60, and 72-73, of the owner's manual.
Whenever you select a Main Voice, Dual Voice, or Split Voice, all of the voice parameters will be reset to their factory default settings for the given preset voice. I have no experience with the DGX-660, but on the PSR-E models that I'm familiar with each preset voice usually has specific default Dual and Split Voices-- as well as default effect types-- which have been chosen by Yamaha to complement the Main Voice, although this varies from model to model. Thus, when you choose a specific preset voice to be the Main Voice, it may automatically change the preset voices that the Dual Voice and Split Voice are set to, along with the Reverb Type, Chorus Type, DSP Type, Harmony Type, and so on, including the various parameters related to each of these, such as Main Volume, Dual Volume, Split Volume, Main Octave, Dual Octave, Split Octave, Main Reverb, Dual Reverb, Split Reverb, and so on.
For this reason, it's best to choose the Main Voice before choosing the Dual and Split Voices, Reverb and Chorus Types, and so on. Then, after you've chosen the specific voices and effects you want to use, you can safely go into the Function menu and adjust the various parameters for the voices and effects.
This also means that you should save any modified settings that you like to a Registration for later recall, since they'll keep getting reset to the factory default settings whenever you choose a different voice. See pages 50-51 of the owner's manual.
There is no way to adjust the volumes of the voices while playing, but if you need to temporarily increase or decrease the volume of the Main, Dual, and/or Split Voice while playing then you could try setting up different Registrations for that, such as setting up Registration 1 so the Split Voice is louder than the Main and Dual Voices, setting up Registration 2 so the three voices are balanced "normally," setting up Registration 3 so the Main Voice is louder than the Dual and Split Voices, and setting up Registration 4 so the Dual Voice is louder than the Main and Split Voices, or something like that, so you can switch to a different Registration to briefly give more emphasis to the Main, Dual, or Split Voice, then switch back to their normal balances.
Note that if you're actually referring to the voices and volumes used by the auto-accompaniment styles, there is no way to alter those on the keyboard. If you're using an external style file rather than one of the internal or built-in styles, then you could try using third-party software to modify the style settings on your computer and save the changes to a new style file.
If you're connecting and using an iPad or computer to your keyboard while playing, you could also try changing the keyboard's Local Control setting to Off-- so the keyboard won't produce any sounds when you play it-- then route the MIDI data from the keyboard to the iPad or computer and then back to the keyboard again. This lets you play the keyboard as though it were a MIDI keyboard controller, use external software on your iPad or computer to "slice, dice, and spice" the keyboard's MIDI data, and send it back to the keyboard to be played as though the keyboard were a MIDI sound module. Doing this would let you modify the Channel Volumes for the Main, Dual, and Split Voices on the fly, as well as making it possible to change the voices and parameters used for the channels of the style.