How do you transfer an IP from one business unit to another?

I have a current SFMC build with one business unit that is looking to split into two. I have the IPs I want to reformat via SAPs and eventually transfer over to the new business unit. We are not ready to split the data at the moment, but I want to use the SAPs to get new domains to differentiate the senders. 

If I use an SAP to change the domain on a pre-existing IP, can that IP move to a new business unit later? Or do I have to change the business unit at the time of implementing the SAP?