Yes, but if the two pets are friends, the cat may run out just behind the dog. If they are not friendly, it works better.
Can I let out my dog but not let the cat go out?
The Best Pet Door
Most pets hate flap doors! PlexiDor Pet Doors are long-lasting and beloved alternatives.They have hinges, like a door, so there's no loud flap slap or flexible materials. They lock easily, and most models come with a steel security plate for additional security when you are away.
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Door Finder
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