What I want to do is to move multiple vertices(upper picture) along the edges and all the other vertices appropriately like subdivide create new vertices(lower pictures). I hope I can move all the vertices along the lines at once where subdivide create vertices if you select more "Number of Cuts" in Subdivide submenu.
In short, I want to Move vertices along the line between inner and outter vertices(upper picture) like subdivde creates vertices along the line. Lower picture is a sample of "subdivde" between inner and outter vertices