In a mess trying to shuffle heading styles to heading levels one below

I have a Word document and I want to change the levels of the headings by moving each down one, but keep the same styles for the headings as they now appear in the document. In other words, I want to apply the style for Title to Heading 1, the style for Heading 1 to Heading 2, Heading 2 to Heading 3, and Heading 3 to Heading 4. I need to do this in order to make section numbering work properly in a document that is a compilation of a number of smaller documents.

Unfortunately, when I do the obvious thing, which is to select one instance of Heading 3 and apply that style to Heading 4, and then select one instance of Heading 2 and apply it to Heading 3, the style currently applied to Heading 2 gets applied to both Heading 3 and Heading 4, when I only want it applied to Heading 3. If I continue the process the whole way, every heading ends up with the same appearance as Title.

Is there a way to shuffle the styles down the hierarchy of headings without making such a mess?

I'm using Office 2019.