Change Z offset of lines

I am trying to change the z offset of lines in unity so it is possible to cover one line with another in 3D space. For a simple case I am generating a 1x1 square on a 2x2 quad.

The code to generate the square is

 using UnityEngine;
 using System.Collections;
 
 public class Test : MonoBehaviour {
     void Start () {
         MeshFilter filter=gameObject.AddComponent<MeshFilter>();
         Mesh mesh=new Mesh();
         mesh.vertices=new Vector3[] { 
             new Vector3(-0.5f, -0.5f, 0),
             new Vector3(-0.5f, 0.5f, 0),
             new Vector3(0.5f, -0.5f, 0),
             new Vector3(0.5f, 0.5f, 0),
         };
         int[] lines=new int[] { 
             0, 1, 0, 2, 2, 3, 1, 3,
         };
         mesh.SetIndices(lines, MeshTopology.Lines, 0);
         mesh.normals=new Vector3[] {         
             new Vector3(-0.5f, -0.5f, 0),
             new Vector3(-0.5f, 0.5f, 0),
             new Vector3(0.5f, -0.5f, 0),
             new Vector3(0.5f, 0.5f, 0),
         };
         filter.mesh=mesh; 
 
         MeshRenderer renderer=gameObject.AddComponent<MeshRenderer>();
         renderer.sharedMaterial=Resources.Load<Material>("Materials/Flat Offset");
     }    
 }

where the flat offset shader is

 Shader "Custom/Flat Offset"{
    Properties {
      _Color ("Color", Color) = (0.0, 0.0, 0.0, 0.0)
    }
    SubShader {
          Pass {
              Offset -1, -1
              CGPROGRAM
              
              #pragma vertex vert
              #pragma fragment frag
              
              uniform float4 _Color;
               
              float4 vert (float4 position: POSITION) : SV_POSITION
              {
                  return mul(UNITY_MATRIX_MVP, position);
              }
  
              float4 frag () : COLOR
              {
                  return _Color;
              }
              ENDCG
          }
    }
    FallBack "Diffuse"
 }

The shader works to fix z fighting between two quads

However this does not fix z fighting between the quad/line.

Is there a way to change the depth offset of lines? I want to make it so one group of lines has a different depth offset from another group of lines (in addition to having a different depth offset than quads).