with another girl?

Not so much weird as self destructive. You have put a time bomb into your relationship which will go off fairly soon. It is a good way to have set up a self fulfilling prophecy to end the relationship. My ex wife allowed the same and it and of course other things led to the end of the relationship. Yes it can be fixed, but not by having an open relationship. The way to fix this is to close off your relationship to others and dedicate yourselves to each other.