I don’t know that it’s one single special effect as much as just weapon’s grade vocal compression (denser) and maybe a little echo/reverb.
Effect > Leveler
Effect > Compressor
Effect > Hard Limiter.
You might apply Chris’s Compressor to the vocal tracks before the other tools. Chris should even out word by word volume variations and make it a little easier for the other tools to work. Crank the first value, compression up to 0.8 or 0.9 or maybe higher. Listen to how it works.
This will be a lot harder if you mixed the voices and music already. Compressors and effects will start pumping the vocals with the bass notes making some words vanish. That’s a valid music technique, but maybe not if you didn’t want that.