No. You Can't. They Are A Business And Will Go The Route That Results In The Smallest Payout. But, . . .
. . . Sometimes if the car is "on the line" between "repairable" and "totalled" your wishes and receipts showing recent repairs / maintenance can sway a decision.
You should be able to take a cash settlement and then purchase the "salvage" (totalled car) from your insurer. Then you are free to get it repaired if you'd like.
Either way, you need to do your homework. The decision to total or repair and the amount of settlement you would recive all hinge on the car's value. Find as many cars as you can that were similar (make, model, miles, condition) and get the retail selling prices in writng (clip ads, print-out ads, etc.). Round up all those receipts that show that your car was recently put into "very good" or "excellent" condition and presnt your case after they make you a settlement offer.
You need to know what their first offer is and how much they would charge to sell you back the salvage. If you've got something else to drive, don't be in a hurry to settle. They usually want these things closed out as soon as possible.
One of several things can happen. Nothing different than where you are now, their reconsidering not fixing the car based on the value you present, or a higher settlement amount for you.
You need to find out if the car is going to be diminished in value by having a tile that shows it was totalled if you decide to buy and fix and see how that sits with you. As others have pointed out, make sure you know up front what it's going to cost to fix it if you go that route.
In many cases and in many states negotiating is all part of this process. Mny people just take what they're told to take and that's up to you. Those recent receipts you've saved could help you. Remember your agent. Any problems dealing with adjusters should be brought to the agent's attention. My agent has helped me with this process several times.