It is possible have a different header for different categories.
First I had to create a page for the categories, renaming it "category" + the category ID Number
So, for example... I duplicated my archive.php file and re-named it category-374.php.
WP now knows, when someone clicks on that category it uses my special page vs. the archive.php.
In "category-374.php" I replaced the line:
<?php get_header(); ?>
with the contents of my modified header.
I found the WP Category Templates page helpful: