There are many ways to make AJAX requests, but because Drupal has its own API, you may want to run that part without any hacks - like AJAX commands and behaviors.
Here is a quick example, of how to call Drupal AJAX programmatically:
var arguments = {
value_1: '',
value_2: '',
value_3: ''
};
var ajaxSettings = {
url: '/ajax-path',
submit: arguments
};
Drupal.ajax(ajaxSettings).execute().then(function (data) {
// Execute things after ajax request.
});
This will post three values to /ajax-path and execute all returned AJAX commands and applied behaviors. It also provides a Promise to run additional things right after the request is done.