Each type of business entity can have different methods for changing its type.
For a sole trader, it is as simple as making an amendment to your governing legislation that allows you to become a partner in the business instead.
For partnerships and limited liability companies, it would be similar to doing the same steps but with another person or people.
There is a different process for limited liability companies and corporations. Limited liability companies need approval from the governing legislation while corporations require more formal documents on top of that, such as an election of directors and changes to the authorizing resolution. There are also more filing fees for both of these types of business entities.