That's exactly what I am trying to do. I have like 7 contracts with my insurance company: 2 vehicles full insurance, 2apartments, travel insurances etc. But they said they can't cover it by default agreement as it says any damage caused "during repairs" is not covered.
I've explained the situation to a manager that these weren't really repairs but a flat tyre accident in the middle of nowhere in Lapland when VW assistance didn't even respond. And original tools supplied simply failed to do the job in such conditions.
They are looking into it as a custom case.
If they reject, they will lose tons of annual pays as I will move all the contracts to other insurance company.
I am all prepared they will deny the case though. I will simply repair it from saving money on some canceled insurances. I am paying like 700euros for a 2nd vehicles that stays in a garage and I don't even drive it much.
All these extra insurances are not really worth it from my observation.
If you feel comfortable about getting a bigger payment on an accident yourself it is wiser in the long run.
You pay them regular smaller amounts that are higher in total in the end.
Cases when you are getting more from insurance than paying them are extremely rare.