Hospitalization in Germany

Hello ,
I just moved to Belgium with my family and I just registered to the mutualite ( CM )
and we expect to do a surgery for my kid with a special doctor in Germany ( our choice to go to that specific Dr )
I am quite sure that it is not easy to convince (CM , christian mutulaite ) to pay for the surgery
But is there's anyway for reducing the amount I will pay for hospitalization ?

Can I pay something or enroll for any private insurance which has European coverage ? to reduce the total cost ?

BR
Mohannad

For a mutual to pay it has to be authorised in advance and treatment not available in Belgium. I would not be optimistic