Get Posts from Custom Meta Query

Add ‘relation’ => ‘OR’ to your Meta Query, I think it will be something like this…

'meta_query' =>  array(
   'relation' => 'AND', // Optional, defaults to "AND"
   array(
        'key' => $country_meta_key,
        'value' => $country,
        'compare' => 'LIKE'
   ),
array(
    'relation' => 'OR',
     array(
            'key' => $state_meta_key,
            'value' => $us_state,
            'compare' => 'LIKE'
        ),
        array(
            'key' => $state_meta_key,
            'value' => $ca_state,
            'compare' => 'LIKE'
        ),
        array(
            'key' => $state_meta_key,
            'value' => $mx_state,
            'compare' => 'LIKE'
        )
)
); 

https://codex.wordpress.org/Class_Reference/WP_Meta_Query