Generally your own insurance policy has a rental car allowance or daily limit for a rental car to provide you with transportation while your vehicle is being repaired. If your car is beyond repair than the rental car period might continue as you negotiate for a settlement for the total loss of your vehicle.

In your situation, the at-fault person's insurance policy should make you whole. That means it is their responsibility to provide you with what you need to be in the same situation you were in prior to the accident. They may try to negotiate an amount, and they may set a limit, but it is your right to require them to provide you with the same situation you had prior to the accident. You have the right to sue the responsible party to make you whole, and that may be the Taxi company, including the insurance company that is representing them.

If it is necessary for you to rent a larger or upgraded vehicle then you can try negotiating the extra cost of this with the insurance company. You can check to see if there are any state guidelines for this sort of thing by contacting the consumer division of your state's insurance regulatory body.