During the 0.7 revamp, the feature was incompatible, but now it's finally coming back.
New Game +
This feature, after you finish the beta, will allow you to restart the story of the game while keeping all your other progress. You will keep the pokemon you've obtained, the eeveelutions unlocked, sidequests completed, etc. You will also keep your items, except for story items like the Pokedex, gym bades, axe, etc.
For balance, New Game + will reset all your Pokemon levels to 5.
This feature will be coming in the next version, which will be named Beta 0.731