I think you want this:
select t.*
from t join
(select field_one, field_two
from t
group by field_one, field_two
having count(*) = 2 -- or do you mean >= 2?
) tsum
on t.field_one = tsum.field_one and t.field_two = tsum.field_two
The subquery finds the duplicates based on the first two columns. The outer query returns the original rows.
If you want duplicates relative to another value, then add that condition to the subquery:
select t.*
from t join
(select field_one, field_two
from t
where field3 = 'no1' -- or whatever you want to set it to
group by field_one, field_two
having count(*) = 2 -- or do you mean >= 2?
) tsum
on t.field_one = tsum.field_one and t.field_two = tsum.field_two