Regarding US patent law. I have an issued patent. If I want…

Those probably don't apply in your situation, It seems you would want a CIP or totally new application, but, this explains it rather well:

A continuation is a patent application filed by an applicant who wants to pursue additional claims to an invention disclosed in the parent application. The continuation uses the same specification as the parent application, claims the priority date of the parent, and generally names at least one of the same inventors as in the parent. This type of application is often filed when a patent examiner has allowed some but rejected other claims in an application, or where an applicant feels that he or she has not exhausted all useful ways of claiming different embodiments of the invention during the prosecution of the parent.

A divisional application, or simply a “divisional”, is filed when the parent application contains more than one distinct invention. If multiple inventions are disclosed in a single application, the applicant may pursue claims to one of the multiple inventions in the parent application, and pursue the other inventions in subsequent divisional applications. The divisional applications generally have the same specification as the parent applications, claim the priority date of the parent, but have a different set of claims. In the U.S., divisional applications often result when the patent Examiner issues a “restriction requirement”, which limits each patent application to a single invention. Divisional applications in Europe and Australia are equivalent to a continuation application in the U.S.