How can I make this code add to the mesh instead of over writing it?

I am trying to make a system like Minecraft where an array of values is used to generate a 32^3 cubic chunk, and I'm working on making it so that all block faces in a 'chunk' are combined as one mesh... except for one problem:

In the code below used to render a face of a block in a given position and rotation, instead of adding a face to the mesh of a 'chunk' it is overwriting that chunk's mesh... So I've tried to make a new mesh on a child and combine them, but that is giving me this error "Combine mesh instance 0 is null" on the first attempt to combine meshes, the following attempts to combine seem to do nothing.

Is there a better way to read the cubic array and make a mesh for the visible faces of the blocks?

 void AddFace (int x, int y, int z, int side){
     MeshFilter mf = transform.GetChild (0).gameObject.GetComponent<MeshFilter> ();
     Mesh mesh = mf.mesh;
     //Vertices!
     Vector3[] vert = new Vector3[4];
     if (side == 0) {
         vert [0] = new Vector3 (x + 1, y, z + 1);
         vert [1] = new Vector3 (x, y, z + 1);
         vert [2] = new Vector3 (x + 1, y + 1, z + 1);
         vert [3] = new Vector3 (x, y + 1, z + 1);
     } else if (side == 1) {
         vert [0] = new Vector3 (x + 1, y, z);
         vert [1] = new Vector3 (x + 1, y, z + 1);
         vert [2] = new Vector3 (x + 1, y + 1, z);
         vert [3] = new Vector3 (x + 1, y + 1, z + 1);

            **Ect...**

     } else if (side == 5) {
         vert [0] = new Vector3 (x + 1, y, z);
         vert [1] = new Vector3 (x, y, z);
         vert [2] = new Vector3 (x + 1, y, z + 1);
         vert [3] = new Vector3 (x, y, z + 1);
     }
     //Triangles!
     int[] tri = new int[6];

     tri [0] = 0;
     tri [1] = 2;
     tri [2] = 1;
 
     tri [3] = 2;
     tri [4] = 3;
     tri [5] = 1;

     //Normals!
     Vector3[] norm = new Vector3[4];
     if (side == 0) {
         norm [0] = Vector3.forward;
         norm [1] = Vector3.forward;
         norm [2] = Vector3.forward;
         norm [3] = Vector3.forward;
     }
             **Ect...**

     else if (side == 5) {
         norm [0] = -Vector3.up;
         norm [1] = -Vector3.up;
         norm [2] = -Vector3.up;
         norm [3] = -Vector3.up;
     }

     //UVs
     Vector2[] uv = new Vector2[4];

     uv [0] = new Vector2 (0, 0);
     uv [1] = new Vector2 (0, 1);
     uv [2] = new Vector2 (1, 0);
     uv [3] = new Vector2 (1, 1);

     //Assign!
     mesh.vertices = vert;
     mesh.triangles = tri;
     mesh.normals = norm;
     mesh.uv = uv;

     //combine!
     MeshFilter[] meshFilters = GetComponentsInChildren<MeshFilter>();
     CombineInstance[] combine = new CombineInstance[meshFilters.Length];
     Destroy (this.gameObject.GetComponent<MeshCollider> ());
     int i = 0;
     while (i < meshFilters.Length) {
         combine [i].mesh = meshFilters [i].sharedMesh;
         combine [i].transform = meshFilters [i].transform.localToWorldMatrix;
         meshFilters [i].gameObject.SetActive (false);
         i++;
     }
     transform.GetComponent<MeshFilter> ().mesh = new Mesh ();
     transform.GetComponent<MeshFilter> ().mesh.CombineMeshes (combine, true);
     transform.GetComponent<MeshFilter> ().mesh.RecalculateBounds ();
     transform.GetComponent<MeshFilter> ().mesh.RecalculateNormals ();
     transform.GetComponent<MeshFilter> ().mesh.Optimize ();

     this.gameObject.AddComponent<MeshCollider> ();
     transform.gameObject.SetActive (true);
 }