meta_query with multiple key

key in a meta query needs to be a string, you can’t pass multiple keys to a single meta query. You’ll need add a query for each key:

$filter = array(
    'post_type'      => 'request',
    'post_status'    => 'publish',
    'posts_per_page' => -1,
    'meta_query'     => array(
        'relation' => 'OR',
        array(
            'key'     => $key1,
            'value'   => $search_value,
            'compare' => 'LIKE',
        ),
        array(
            'key'     => $key2,
            'value'   => $search_value,
            'compare' => 'LIKE',
        ),
        array(
            'key'     => $key3,
            'value'   => $search_value,
            'compare' => 'LIKE',
        ),
    ),
);

Note that I set 'relation' to 'OR' so that results will be returned for posts that match any of the keys, rather than all. If you need results to have matches for all the keys, change it back to 'AND'.