post, an existing series can be extended within a themed anthology either by its creator or by another author. Thus:
Poul Anderson contributed to an Asimov-themed anthology by adding to Asimov's Robots series;
several other writers contributed to that anthology by adding to later periods of Asimov's future history and to one or two other series;
Anderson both contributed to a Knights Templar themed anthology and added to his Time Patrol series by having a Time Patrolman infiltrate the Knights;
several authors, including SM Stirling, contributed to an Anderson-themed anthology by adding to different Anderson series;
Stirling contributed to an alternative histories anthology by adding to his Angrezi Raj alternative history;
Stirling contributed to a retro-Mars anthology by revisiting the terraformed Mars of his "Lords of Creation" alternative history;
Matthew Hughes contributed to that retro-Mars anthology by adding to Ray Bradbury's Martian Chronicles;
Isaac Asimov both contributed to a Batman anthology and added to his Black Widowers series by having the Black Widowers invite Bruce Wayne to dinner;
several authors, including Stirling, contributed new stories to a Barsoom anthology.
And I am always more interested in particular additions to existing series than in the themed anthologies as such.