Correctly Overriding Functions

I'm quite new to Omeka, and still orienting myself to the way omeka approaches certain functionality, so if this question is obtuse or I've placed it in the wrong forum, I apologize! Any help you can provide would be greatly appreciated.

I've been working on customizing a theme to match the needs of my current project, using ExhibitBuilder, and have begun to move past basic theme edits. As more specific tweaks are needed to achieve the intended functionality I am finding that I do not know how Omeka handles that level of modification? Is there a built in structure for supplanting custom versions of core functions from the theme end? I would really like to not have to edit the core files, or ExhibitBuilder's core files, but from what I have seen, is there another way to change how certain functions operate?

For Example, if one wanted to modify Exhibit_Builder_Display_Item() what would be the best way to do that? Editing it would change the core plugin, leading to problems with updating, and writing a new function would require changing the call everywhere it happened. I've had some experience with Drupal, where there is a "functions.php" file which can replace default functions with theme specific ones. Does Omeka have any functionality similar to this?

I realize I've rambled through the description, basicly, I am interested in how people deal with needing to modify existing functions without compromising the base code. Agian, ny insights you could provide would be of much help! Thanks.