In almost all cases, no. When you settle a car accident claim, you sign a release — a document that gives up your right to seek anything more for that crash in exchange for the payment. Once it is signed, the claim is generally closed for good, even if your injuries later turn out to be worse than expected.
That is exactly why settling too early is so risky. If you accept an offer before your injuries are fully understood, you usually cannot go back for more once the true extent becomes clear. Understanding your claim before you sign is the protection.
There are narrow exceptions — such as fraud or certain mistakes — but they are limited and hard to invoke. The far safer approach is to make sure a settlement is right before you agree to it, rather than counting on reopening it later.