Pretty sparse on details here but I think you could do something like this. I'm not so sure about the "simple" part but it should work.
select * from
(
Select *
, case when condition1 then 1 else 0 end
+ case when condition2 then 1 else 0 end
+ case when condition3 then 1 else 0 end as ConditionCount
from table_name
where
condition 1
OR condition 2
) x
where ConditionCount >= 8
This is is a rather strange scenario. 😀
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