How to change the pagination of related entities displayed on a taxonomy term page?
The taxonomy module uses the default_nodes_main variable to decide how many to show per page (this happens around line 55 of taxonomy.pages.inc in case you're interested).

Usually you would implement a custom module and provide a form to override that variable for your users. But you don't have to do that, if you just want to set the variable once and be done with it use one of the following methods instead:


Use Drush (drush vset default_nodes_main 20)
Add a PHP snippet somewhere that will be run in your site (you only need to do it once)

variable_set('default_nodes_main', 20);

Use the Devel variable editor