Yes, this seems to be a problem with the new interface forms that a few of my Airtable consulting clients have been stumbling upon as well. It was definitely frustrating for them.
Until Airtable fixes this issue, the #1 perfect solution for this problem is to use Fillout’s advanced forms for Airtable.
Not only is Fillout 100% free, and not only can you open multiple prefilled forms simultaneously (each one in their own tab), but get this: YOU NEVER HAVE TO PREFILL FORMS AGAIN, because Fillout gives you the ability to directly update Airtable records from a form!
Fillout also offers dozens of advanced Airtable-specific features that you can’t get from Airtable’s native forms, such as displaying lookup fields & formulas & rollup fields & existing attachment images on forms, creating new linked records on a form, visually displaying as many fields as you want to see in a linked record selection list, limiting the number of linked records that can be chosen, multi-page forms with conditional paths, accepting payments on forms, and dozens of other advanced Airtable-specific features that are not available in Airtable’s native forms.
I give a brief demonstration of Fillout on this Airtable podcast episode.
p.s. If you have a budget for your project and you’d like to hire an expert Airtable consultant to help you with any of this, please feel free to contact me through my website: Airtable consulting — ScottWorld
Ah...this is a feature to let users resume partial form submissions and I'm not aware of a way to turn it off, and I don't think you can turn it off via URL params either
Assuming the link is accessible to anyone on the web, you could try opening the form in a private tab perhaps? That would give you two forms at least, and if you needed more you could use another browser and yet another private tab hah
If you do end up using Fillout note that it allows the resuming of partial submissions by default, and you can turn it off by going to Settings -> Form Behavior

While you CAN turn off that setting in Fillout — and it might be a good idea in this circumstance — you don't really need to worry about turning off that setting, because Fillout will always give the user the option of starting a new form in a new tab, so you can have multiple different forms open in multiple different tabs.
Yes, this seems to be a problem with the new interface forms that a few of my Airtable consulting clients have been stumbling upon as well. It was definitely frustrating for them.
Until Airtable fixes this issue, the #1 perfect solution for this problem is to use Fillout’s advanced forms for Airtable.
Not only is Fillout 100% free, and not only can you open multiple prefilled forms simultaneously (each one in their own tab), but get this: YOU NEVER HAVE TO PREFILL FORMS AGAIN, because Fillout gives you the ability to directly update Airtable records from a form!
Fillout also offers dozens of advanced Airtable-specific features that you can’t get from Airtable’s native forms, such as displaying lookup fields & formulas & rollup fields & existing attachment images on forms, creating new linked records on a form, visually displaying as many fields as you want to see in a linked record selection list, limiting the number of linked records that can be chosen, multi-page forms with conditional paths, accepting payments on forms, and dozens of other advanced Airtable-specific features that are not available in Airtable’s native forms.
I give a brief demonstration of Fillout on this Airtable podcast episode.
p.s. If you have a budget for your project and you’d like to hire an expert Airtable consultant to help you with any of this, please feel free to contact me through my website: Airtable consulting — ScottWorld
Thanks for the reply, I agree Fillout is great form software and works well on a retail site but the forms we are using are internal and used many times daily. Fillout is a little slow pulling single select data lists from airtable and cannot compare to the speed of using the interface forms....
Hopefully, Airtable will add some kind of option to switch on/off for remembering incomplete form data soon
In the meantime switched back to using the legacy form version which seems like madness!