If the staff of one office merged with the staff of another office, the combined were staff. There might be 99 staff working in a building. Marketing and sales staff might attend a conference. The constant being the word ‘staff’.
Chambers Dictionary does have a plural of ‘Staffs’, as does Macmillan Dictionary. Merriman Webster does have ‘staffs’ as a plural for some uses but ‘staff’ as plural in sense of ‘three full-time staff’.
I still do not like the look or sound of ‘Health Services Staffs’. I cannot see myself using the plural form anytime soon.