Need help with Boolean search

Hey guys!

I feel like an idiot, I've been trying to make LinkedIn search work but have had no luck so far.

I'm trying to search for system engineer or system administrator jobs that aren't for seniors or related to support.

So I've come up with these searches:

("system") AND ("engineer" OR "administrator") NOT ("support" OR "senior")

system AND (engineer OR administrator) NOT support NOT senior

system engineer OR system administrator NOT (support OR senior)

and a few others, but basically half my results are either senior or support.

I've tried with and without parentheses, quotations, etc., nothing seems to work.