I am familiar with overriding templates modules etc using ...yourtemplate/html/.......
Below are comments from a very handy add on for K2
Are there any event triggers that can be used to add code from another directory instead of changing core files?

From K2 community post "Unfortunately I haven't found any way to provide the functionality I was looking for solely using Joomla module, thus I had to add another listing method 'filter' to the K2 core. You will have to overwrite some of K2 files to use the module."

From: documentation of component
models/itemlist.php:

* added method 'filter' at lines 105 and 356
* added code to destroy items in the results array ($rows) which are not meeting filtered (searched for) criteria at line 248 before returning the array.

views/itemlist/view.html.php

* added handler 'filter' at line 181

views/itemlist/view.feed.php

* added handler 'filter' at line 91

sef_ext/com_k2.php

* added handler 'filter'

Module body:
(folder /modules/mod_k2_filter/)

includes/filtermethod.php