Each value needs to be a separate meta query
'meta_query' => array(
'relation' => 'OR',
array(
'key' => 'linked_outcomes',
'value' => '"value 1"',
'compare' => 'LIKE'
),
array(
'key' => 'linked_outcomes',
'value' => '"value 2"',
'compare' => 'LIKE'
)
)