Historical Rules · 14 June 2019
Rule 103.4b
Official source text from the 14 June 2019 Rules release
If an effect allows a player to perform an action “any time [that player] could mulligan,” the player may perform that action at a time they would declare whether they will take a mulligan. This need not be in the first round of mulligans. Other players may have already made their mulligan declarations by the time the player has the option to perform this action. If the player performs the action, they then declare whether they will take a mulligan.