"the staff which" is grammatically correct and usable in written English.
You can use it to refer to a specific group of people. For example, "The staff which works in the department is highly capable."
The staff, which mirrors the clientele, is willing to please.
The staff, which used to be European, is now Egyptian.
I oversee the staff, which right now is 15.
"The news rocked the staff, which has been divided about Weiss's leadership," she wrote.
There is little question among the staff which camp Mr. Stringer is in.
He is generally liked by the staff, which recoiled at Mr. Kelly's military style.
The dolphins' departure, though, will be difficult for the staff, which had grown attached to them.
The real sweetness, though, is in the staff, which is exceptionally warm and attentive.
So is most of the staff, which was too afraid to come to work.
It is the morale and expectations of the staff which have really rotted.
The staff — which included Smith's bodyguard and his cousin — kept crazy hours and fought non-stop.
