As intriguing as the concept may sound, based on our current understanding of quantum mechanics, it is not possible to use quantum entanglement to communicate with other beings, whether they are in parallel universes or not, including your cat.
Quantum entanglement is a phenomenon that involves the correlation of quantum states between particles. While it allows for non-local correlations between entangled particles, it does not provide a means of instant communication or information transfer. The act of measuring or manipulating one entangled particle does not allow you to directly convey information to another entangled particle, especially not to a cat in a parallel universe.
Quantum entanglement is subject to certain fundamental limitations, such as the no-communication theorem. This theorem states that it is impossible to use quantum entanglement to transmit information faster than the speed of light. Even if you were able to entangle particles with a cat in another universe, you would not be able to use that entanglement to communicate or interact with the cat in any meaningful way.
It's important to distinguish the concept of quantum entanglement, which is a well-established phenomenon in quantum mechanics, from the notion of using it for communication or interaction with other beings or parallel universes, which goes beyond the current scientific understanding and technological capabilities.