Looking at the remaining games here are some scenarios:
West Coast must lose every game to get a priority pick - if they do that then North have 5 wins, Richmond and Fremantle have a minimum of 4.
North must lose every game to get a priority pick - if they do that then West Coast have 5 wins, Richmond have a minimum of 4, Melbourne have a minimum of 3.
Fremantle can win one more game and still get a priority pick - if they don't then then West Coast have 5 wins.
Richmond can win one more game and still get a priority pick - if they don't then North and West Coast have 5 wins, Melbourne have a minimum of 3.
Melbourne can win 2 more games and still get a priority pick - if they don't win any then North have 5 wins, Richmond and Fremantle have a minimum of 4, only 2 of Richmond/Fremantle/West Coast can stay under 5.
It's only possible for a maximum of 4 teams to get a priority pick.
Here are the 'affected' games:
R16 - Richmond vs North
R17 - Fremantle vs West Coast
R18 - Melbourne vs Richmond
R19 - North vs Melbourne
R20 - West Coast vs North
R20 - Melbourne vs Fremantle
R22 - West Coast vs Richmond