In a three player game:
- Player A plays a Yellow +2 Card
- Player B picks up 2 cards
- Player C plays a Green +2 Card
Is player C allowed to change colors, on the basis of a punishing card?
Yes, Player C can play a different colored Draw 2 Card on top of Player A's Draw 2 Card.
Draw 2 Card - ... This card may only be played on a matching color or on another Draw 2 card.
Here's a great place to read the rules yourself:
From mattel.com: https://service.mattel.com/instruction_sheets/42001pr.pdf