Nested Queries of decreasing specificity

This answer just explains a possible approach and doesn’t provides with detailed code.

The following approach relies more on PHP for filtering the results instead of multiple WP_Query, it uses a single WP_Query along with multiple get_post_meta() calls.

Step 1:

For the current post build an array using get_field() or get_post_meta() with all the necessary key and values:

$current_post = array(
   k1 => v1, 
   k2 => v2, 
   k3 =>v3 
);

Step 2:

Get all the post Ids using WP_Query(meta_query) which has at least one matching key,value pair.

WP_Query[
'meta_query'    => array(
        'relation'      => 'OR',
        array(
            'key'       => 'k1',
            'value'     => 'v1',
            'compare'   => '='
        ),
        array(
            'key'       => 'k2',
            'value'     => 'v2',
            'compare'   => '='
        ),
        array(
            'key'       => 'k3',
            'value'     => 'v3',
            'compare'   => '='
        )
    )
]

Step 3:

For all the post ids from above result; iterate and build an array matching_posts with all the key, values;

$matching_posts = array(
     post_id_1 => array ( 
       k1 => v1, 
       k2 => v2, 
       k3 =>v3 
     ),
     post_id_2 => array ( 
       k1 => v1, 
       k2 => v2, 
       k3 =>v3 
     )
     .
     .
     .
    );

Step 4:

4.1 :

Use php array functions[array_intersect] to get related post ids for $current_post[];

Remove related post ids from $matching_posts[]

4.2 Remove the last key=>value from $current_post[]; and repeat 4.1

Repeat 4.2

This would give you 3 sets of array:

1. Post ids with all key=>value(3) in common,
2. and then 2 same key=>value
3. And then posts which has only single key=>value in common.

For the other part of question: getting at least n posts for the current post, you can have a simple query to get n - x posts which excludes all the post above. Where x is the sum of all matching posts.