Historical Rules · 27 March 2015
Rule 103.4b
Official source text from the 27 March 2015 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 he or she would declare whether or not he or she 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, he or she then declares whether or not he or she will take a mulligan.