How can I let people submit multiple responses to a subset of questions?

After entering the Name/email/etc...I want them to be able to submit 1 or more (depending on the respondents preference), entries to another set of questions without having to refill all the other information

You can have your form to redirect back to the form itself so when the user submits, the form redirects back to the default state where users can submit another entry. This is possible when you enter your form URL as the external thank you URL. Guide: How to Redirect to a Page After Form Submission. Unfortunately, the user will have to enter everything again since the fields are cleared whenever the form is submitted.

If you're looking for a feature where users could add another entry by simply duplicating the fields predefined group of fields, you can use this widget https://www.jotform.com/widgets/configurable-list.