This is Rae from Shopify. Thanks for reaching out for help with gathering these details, and welcome to the Shopify Community.
Shopify's checkout is a completely secure form that cannot be edited, or added onto in any way, in order to ensure the form remains safe and secure. However, I understand that it's necessary to gather these extra details from your customers, so I recommend collecting these in your cart page instead, rather than in the checkout.
If you need any extra help with adding cart attributes, or if you'd like to speak with someone about adding them on your behalf, I recommend reaching out to Shopify Experts for more information. Experts are third party designers and developers who are very skilled in our platform, so they're the best people to speak with about adding additional coding, or creating extra features for your specific site, if cart attributes don't fit your exact needs.
Additionally, there are several apps like Required by The Resistance and Customer & Cart Attribute that can be used to collect details from customers in your cart page. These are third party apps, so if you need any assistance with setting them up, or if you have questions about using these apps, I suggest reaching out to the app developers directly for more help. You can contact them by following these steps.
Can you please tell me a bit more about why you're looking to add this feature? Are you selling products only to other businesses? I'd love to hear more about your plans!