At the beginning of the next end step, exchange life totals with that player, exchange control of all permanents you and that player control, and exchange cards in your hands, cards in your libraries, and cards in your graveyards
Famous catchphrases and events, like Blood for the Blood God and Exterminatus, also seem to be the basis for many cards
Just choose to interweave the deck halves such that the same half always remains on top, and you can actually multiple cards to stay in the same position throughout the whole shuffle
You could even take two different commanders that share a color, and build a larger module for each that allows you to swap between commanders while keeping the same base theme intact
You cant just swap basics between opponents and ruin their mana bases
So, unlike Eldrazi, where getting rid of Eye of Ugin turned the deck from an oppressive monster into just another tier-one deck, I'm not sure this is possible with Dredge