I have gotten a few random events that said one of my pets had gotten more space in their treasure chest. It has happened a few time to different pets of mine. How can i tell how many items can be put in their treasure chest? How many items can i put in their chest without the random events?

They all start out with 3 slots. There is no way of knowing how many slots they currently have, you'll need to fill them up till you get the message that it's full.

Thanks! my pet LittleLorene has 9 items in her treasure chest. Not sure how she got so many.