Hello Tom,
If you go to the Form edit page, click the three dots collapse button to open the settings pane, you can select “One response per person” option.
However, please notice that this option is only available when you set “Only people in my organization can respond” but not “Anyone with the link can respond”. To explain this, when you select “Anyone with the link can respond”, a response is anonymous, no personally identifiable information, such as name or user ID, is stored. In this scenario, Microsoft Forms can’t identify the people who submit the response is, so it will not be able to control whether it allows to only one response or multiple responses from that specific person.
Unfortunately, with a setting “Only people in my organization can respond” the users will have to sign in with work or school account created within your Office 365 tenant and **** the external users won’t be able to answer a form. So, there’s nothing to do to invite potential respondents to join organization unless you create an account for them.
That means, the limit response feature doesn't work for external users currently. This is a feature limitation.
For more settings supported for Microsoft Forms, you can refer to Adjust your form or quiz settings in Microsoft Forms.
Summarizing the answer, I’m afraid this is impossible to create a form “Anyone with the link can respond” and restrict the answers to one per user. We do understand the inconvenience caused and apologize for it. So, to address your concern about the situation, we’d suggest you kindly leave a feedback: in MS Forms select More form settings (…) > Feedback.
Best Regards,
Igor