In the control panel for CiviCase by default you see activities scheduled for the next two weeks under "My upcoming activities".
Is it possible to extend or control this timeframe? If so, how?
The definition is hardcoded in the view. See CRM_Case_BAO_Case::createCaseViewsQuery().
So you need to change the mysql view definition in the database. Copy and paste the "CREATE OR REPLACE..." code in the above function into phpmyadmin (or whatever) and change the 14 as desired. But it might get changed on upgrades if that view definition changes.
The original spec said "default", but then making it configurable I expect was just time/budget/priority.
See also How can I modify what is displayed on the civicase dashboard?