Du kan prova med group by
och having
klausuler:
select t.user_name, t.thread_id , count(*) as max_count
from tbl t
group by t.user_name, t.thread_id
having count(*) = ( select count(*) as ttl
from tbl
where thread_id = t.thread_id
group by user_name
order by ttl desc
limit 1 )