Is there a filter that runs before the_content?

I want to do some processing of post data as it's displayed, but it needs to run before the_content because I want to muck around with the more tag.

Here's what WordPress does:

function the_content($more_link_text = null, $stripteaser = 0) {
    $content = get_the_content($more_link_text, $stripteaser);
    $content = apply_filters('the_content', $content);
    $content = str_replace(']]>', ']]>', $content);
    echo $content;

As you can see, WP calls get_the_content (which includes more tag processing) BEFORE it calls the apply_filters function for all the the_content filters.

I essentially want to insert a more tag into the post display dynamically, and have it picked up by the_content for processing. So I need a filter that triggers as the content is removed from the database and before get_the_content is called.

Obviously, I could hack the above code, but I'd really prefer not to touch the WordPress core.

Or... is there a best-practices PHP way I can code my own the_content function in a plugin that orverrides, then calls the WordPress function?

Any ideas?