Hello, I am Keith, one of the experts on Just Answer, and pleased to be able to help you with your question.
There is nothing to stop you registering another company or, indeed, being a director thereof. This second company will, of course, be a different legal entity to the original.
Your question is silent as to whether your mean a new registration for VAT, or for a new registration with Companies House, but in any event the answer is the same in both cases.
I do hope that you have found my reply of assistance.
Thank you for your support.