Create custom date range based on day of week?

You can do some rolling custom ranges... for instance, I created 6 custom date ranges for "1 week ago (M-S)", "2 weeks ago (M-S)", up to "6 weeks ago (M-S)"

So that we could do up to a 6 week lookback for custom Monday to Sunday weeks (rather than our standard Sunday to Saturday weeks).

So I took a look at your definitions, and as long as you are using the standard Saturday to Sunday setup... these should work:

First Day of Year - First Saturday of the Year

Note that I changed the "End" definition to "Start of" rather than "End of", to ensure that this didn't go into the second week.

Which results in:

First Day of Year - Second Saturday of the Year

Similar to the logic of the first (except that I did plus 2 weeks):

Which results in:

Unfortunately,  the logic doesn't work with relative dates... it is still locked to Jan 1-7 as those are "relative" to this year... and we will have to wait about 5+ months to see if the logic works next year without relative dates....

Depending on what you are trying to do.. sometimes you can get much better control by using Report Builder and using Excel formulas to set up date calculations, then use the "Date from Cells" to pull data based the calculated dates (but this does mean taking your data out of the Adobe environment...)