You can minimize the distances between 3 points that each belong to a torus :


    res = NMinimize[
            Norm[torus1[x1 , y1] - torus2[x2 , y2]] 
          + Norm[torus3[x3 , y3] - torus2[x2 , y2]],
          {x1, y1, x2, y2, x3, y3}]

    (* torus1[x1 , y1] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
       torus2[x2 , y2] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231}
       torus3[x3 , y3] /. res[[2]]  -->  {10.5868, -2.73435, -2.34231} *)

The 3 torus and the point :

![enter image description here][1]


  [1]: https://i.sstatic.net/UzqLG.jpg