There are two limits in the mobile versions of VF2. To make sure that the game doesn't consume too much memory, your family may have up to 500 total items, which includes all furniture, decor items, and pets. The items in the decor tray are included in determining when your family has reached that limit. Your family is also limited to 30 pets, so that the game doesn't slow down.
When either of these limits is reached, you will receive a message from the game that lets you know that you need to sell some items (or pets) before you can purchase more.
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Barbara
Unicorn
Last Day of Work