How to bevel a concave edge?

Question

I would like to "Bevel the face", like so:

I would like the result to be like the one below created by scaling new edge-loops cut by hand and so not very precise.

If is it possible to do so with a modifier and not via geometry would be amazing.

Answer 1

You can add another loopcut and bevel it.

1. Add a loopcut to the upper part
2. Add a Bevel modifier (limited to that loop)
3. Scale the loopcut down and adjust the bevel

^{I limited the bevel by Weight, but you can also use vertex group}