Hey Jason -
Sorry to be the bearer of bad news. This is a snap if you're dealing with Tableau Server, but hard if you only have the ability to use Desktop/Reader.
Essentially, you'd need to manually create a distinct, filtered extract for each of your colleagues. Then, you'd bring that extract in as a second data source and use the "Data | Replace Data Source" command to tell the report to use your extract instead of the original data source.
Now you can delete the original data source in the workbook.
Each week, you'd deliver a new, personalized extract for the people using Desktop and/or you'd create a new/personalized TWBX using the updated extract for folks who only have Reader.
Clear as mud?