set multiple taxonomy values programmatically
You could also implement the "hook_views_pre_view" function in order to alter the contextual filter arguments of your view and display. In order to add multiple taxonomy values for the same argument, you can change the $args[0] element from the $args variable of the hook.
For example: $args[0] = '22+14+64';
Remember to check the "Allow multiple values" option of the contextual filter.

Take into account that altering contextual filter arguments inside the previous hook may produce troubles when using a views exposed form. Specifically, the form "action" attribute may have a wrong URL. If that issue appears, you can solve it by implementing the "hook_form_views_exposed_form_alter" function and changing the $form['#action'] element with the correct URL.