For example say the gravitation constant instead of equaling G, was actually a range bounded between 0 and infinity.
Our Universe would be at a point on this range (equal to our G value) where things could physically exist and produce stars, galaxies and life. Yet in the gravitation constant's dimension it is able to be lower and higher then our G value.
All other physical constants being equal, this would allow the sort of full universe we recognise to exist on only a very tiny part of the full range of the gravitation constant's dimension. The rest of the dimension would be full of non-universes that would not be able to support anything.
The other non-dependent physical constants perhaps also represent dimensions. And there might even be a set of useful life supporting universe's on a continuous 'line' inside this n-dimensional structure.