If I need to allow only a specific number of responses, how can I configure the form to remove the 'Submit another response' option once that limit is reached?

Google Forms does not have a built-in feature to dynamically close based on the total number of submitted responses. However, you can achieve this with a combination of Google Forms and Google Sheets (linked to the form). You can then use a script in Google Sheets, triggered by a form submit, to close the form by unpublishing the form itself. Look for tutorials on Google Apps Script for closing google forms automatically.