Both CCOVICH and Brendan may have been a little hasty in their replies (if they are saying 'no' you can't have have two mortgages on the one property with different lenders).
It is possible to do, in your case NIB would have a 'first legal charge' on your property up to the amount of the mortgage you would leave outstanding with them and then INBS would have a 'second legal charge' on the property for the sum owing to them. Not often used nowadays, but it is possible to do.
Whether you can gain from a potential INBS windfall I'll defer to those wiser than I to answer that part..........
BM