Changing hospitals midway

Hi, currently I’m doing checkups via the public route at KKH. The next scans are at the week 20 mark. I understand the 20th week scan to be a rather detailed one. Am thinking of registering myself with a Private OBGYN. Anyone could share advice if I should transit before my 20th week scan or after I have completed the 20th week scan at KKH? Any difference if I do it before or after?