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Good question...in most cases, when a party (person or company) offers to settle a potential lawsuit, if they provide a check and you cash the check? That completes the transaction (you can not then sue them for more money)
What you are describing, if the company in question damaged your car, they are responsible for "reasonably foreseeable expenses"...this would include rental car costs or other costs associated with the damages.
If you want to sue them ?
Then do not cash the check...since if you do, that will prevent your lawsuit
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