Spanning Class Across Files?

I’m developing a plugin. I started out with one PHP file (my-plugin.php) containing all the code, but it is becoming unwieldy so I moved various functions into other files (my-post-types.php and my-metaboxes.php).

Now I’m using require_once to include the files in my main PHP file but I’d like for these functions to still be within the main class (MyClass) used in my original PHP file (my-plugin.php).

I assumed at first that they would be, but don’t think this is true b/c when I moved them into separate files I began getting errors regarding the way I’d setup add_action. Specifically, before when everything was in one file I had the following:

add_action( 'init', array( $this, 'register_custom_post_type_series' );

And this was necessary in order for the add_action to operate within the class. But after I moved them into their own files I had to treat them as if they were outside of the class in my add_action, like so:

add_action( 'init', 'register_custom_post_type_series' );

If I shouldn’t be using a single class here, I’m open to hearing about that too…or being directed to articles which help explain how I should be doing this. Any help is appreciated!

Thanks,
Dave