Multiple continuous message notifications from same person

No. You could completely silence the conversation or use focus to prevent or allow notifications from specific contacts, but there's no way to accomplish what you're asking for.

Personally, I have my driving focus to only allow message notifications from a select few family members. Wife, mother, father in law, adult children, sister. They are the only people who would need to contact me that I would want to hear from immediately. everyone else gets the notification that I'm driving and won't be notified. They can override that if it's truly urgent, or they can just call me.

And I also suppose you could experiment with Shortcuts to do something like this:

• Create an Automation that activates when you receive a Message from the person.
• Turn on Do Not Disturb after you get the first message
• Set a Wait period for an amount of time you do not want to get notified of subsequent Messages
• Turn off Do Not Disturb.

This would provide a cooling off period of time after the first message where they will still have the option to Send Anyway like stated by KiltedTim, but will alert them that you do not want to be bothered while Do Not Disturb has been activated for the amount of Wait time you set after they send the first message. This is not exactly what you are looking for, but may help in changing their texting behavior.

I guess it will depend on whether you want to see notifications of there messages immediately all the time, or only if it's really urgent.

If you have auto-reply turned on for your contacts (or favorites if that's more appropriate) and do not explicitly add them to the allowed list for messages in the focus, they will be notified that you are driving and told how to override it to deliver the message immediately if it's urgent.