These need to match, but don't:

apply_filters( 'document_template', $path, $template );

and

add_filter( 'documents_template','my_template', 10, 2 );

document_template != documents_template

Otherwise, everything looks correct.

Edit

Wait, not everything looks correct. I don't think you want to add a parameter to your callback function definition. Instead, you need to define $template within the callback, or simply pass it back unmodified. So, replace this:

function my_template( $template = '' ){

...with this:

function my_template(){

e.g.:

function my_template(){

      $path = MY_INCLUDES_DIR . '/document/'. $template;

     return $path;
}
add_filter( 'documents_template','my_template', 10, 2 );

These need to match, but don't:

apply_filters( 'document_template', $path, $template );

and

add_filter( 'documents_template','my_template', 10, 2 );

document_template != documents_template

Otherwise, everything looks correct.

Edit

Wait, not everything looks correct. I don't think you want to add a parameter to your callback function definition. Instead, you need to define $template within the callback, or simply pass it back unmodified. So, replace this:

function my_template( $template = '' ){

...with this:

function my_template(){

e.g.:

function my_template(){

      $path = MY_INCLUDES_DIR . '/document/'. $template;

     return $path;
}
add_filter( 'documents_template','my_template', 10, 2 );

Edit 2

Okay, minor mistake on my part. Try this as your callback:

function my_template( $path, $template ){

      $path = MY_INCLUDES_DIR . '/document/'. $template;

     return $path;
}
add_filter( 'documents_template','my_template', 10, 2 );

These need to match, but don't:

apply_filters( 'document_template', $path, $template );

and

add_filter( 'documents_template','my_template', 10, 2 );

document_template != documents_template

Otherwise, everything looks correct.

These need to match, but don't:

apply_filters( 'document_template', $path, $template );

and

add_filter( 'documents_template','my_template', 10, 2 );

document_template != documents_template

Otherwise, everything looks correct.

Edit

Wait, not everything looks correct. I don't think you want to add a parameter to your callback function definition. Instead, you need to define $template within the callback, or simply pass it back unmodified. So, replace this:

function my_template( $template = '' ){

...with this:

function my_template(){

e.g.:

function my_template(){

      $path = MY_INCLUDES_DIR . '/document/'. $template;

     return $path;
}
add_filter( 'documents_template','my_template', 10, 2 );