Bevel edge without deleting adjacent edges

Hey, so I have this object where I want to bevel this edge (marked in white):

But if I try to do it, the next edges won’t let me go further as they are there, but I can’t remove them as they form a curvature, anyone knows how?

Thanks in advance!

That is not possible with bevel modifier on a already curved surface.
There is a manual way with snapping to the desired curve or
you can bevel it on a straight face and then use modifiers and go from there.

extrude_and_snap.blend (119.9 KB)