They cannot play on a phase laid down by another player on the same turn they played their phase.
When a player lays down their phase, they may also 'play' on the phase.The entire phase must be played at once, so if the player is on the 1st phase, they must play 2 sets of 3 cards at once. A player who has collected all of the cards needed to complete the entire phase may lay down the phase on their turn.A player may choose to either (1) pick up the top card on the discard pile or (2) draw a card from the draw pile.