KiCad 5.1: New footprint from existing footprint
Short answer: Yes.  @Indraneel's comment is exactly correct.

Long answer with steps:

First create a new library into which you want to save the modified footprint. You do this from the File menu.



Next, choose where you want to save the library and specify what type of library you are creating.  A project library is accessible only from the project you have open.  A global library is accessible from all projects on your computer.  As a general rule, I only create project libraries.  I usually copy the global footprint into my local library when I use it in my projects.



After you have created the new library, it will be listed in the Tree on the left.  Next, you find the footprint you'd like to copy and right-click on it's name.  Then select "Save As"



You will then be presented with a list of the footprint libraries.  You select your newly created library and click OK.