Can I save my car from being written off?

my car was 15 years old with high mileage but iv owned it for 7 years and it was in sound condition and was perfectly good car. I was in a rear end collision the other person ran into the back of me while I was stationary and basically I think my car will be a write off. The visible damage (car yet to be... show more my car was 15 years old with high mileage but iv owned it for 7 years and it was in sound condition and was perfectly good car. I was in a rear end collision the other person ran into the back of me while I was stationary and basically I think my car will be a write off.

The visible damage (car yet to be inspected)
tail gate destroyed
rear bumper destroyed
both rear lights destroyed

the problem I have is that as long as the chassis isn't damaged and everything mechanical is still good these parts(bumper,tailgate and lights) could be replaced with salvage parts quite cheap but the insurance companies repair guys will quote cost based on factory parts and that will exceed the vehicles value so they will want to write it off can I save it if i can get a cheaper quote myself using salvage parts?
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