Many Stories Mansion

From BoardGameGeek:

Please knock twice before entering. Pass by the table where a card game is in full swing under gentle lighting, and grab yourself a warm cup of coffee. Then come meet me on the balcony where palm trees sway. If you haven't lingered too long on the lower floor, would you join me upstairs? Follow the spiral staircase all the way to the rooftop. This is a house of cards. It's time to build it-one story at a time, each floor filled with stories of its own, stacked by your own hands. Many Stories Mansion is a game that blends ladder climbing with polyomino-style puzzles. Each player receives 15 cards from five different colors-there are no numbers-and the order of cards in hand may not be rearranged. On your turn, you must play a combination that beats the previous one. There are only two types of combinations: all cards of the same color or all cards of different colors. The cards you play are placed into your personal area, stacking like blocks to gradually form a tall and vibrant house. The higher you build your mansion, and the more polyomino patterns you complete, the more points you score. The game ends when two players empty their hands, so you'll need to carefully balance between constructing an efficient house and shedding your cards quickly. -description from the designer