How to widen the bevel width? I want to have the bevel more wider than it could be, but the geometry limits the bevel to a limit, when exceeding the limit the faces intersects with each,like follow

The red arrow points to its limits, when I want to bevel more, faces got intersected

How can I make the points meet each other at a far position so the bevel can can be wider?
The top face is an n-gon (it's defined by more than 4 vertices) and problems with beveling n-gons are to be expected. You can move the n-gon inside, by selecting that face and insetting it. As you move it toward the middle, you will experience a different issue, where the edges are going to intersect, so at some point you stop insetting (click to accept), and then scale the face down to further decrease it. Now there's plenty of room using quad topology for the bevel.