If G is a graph with vertex set V (G), then let N[u] be the closed neighborhood of the vertex u 2 V (G). A total double Italian dominating function (TDIDF) on a graph G is a function f : V (G) ! f0; 1; 2; 3g satisfying (i) f(N[u])  3 for every vertex u 2 V (G) with f(u) 2 f0; 1g and (ii) the subgraph induced by the vertices with a non-zero label has no isolated vertices. A TDIDF is an outer-independent total double Italian dominating function (OITDIDF) on G if the set of vertices labeled 0 induces an edgeless subgraph. The weight of an OITDIDF is the sum of its function values over all vertices, and the outer independent total double Italian domination number oi tdI (G) is the minimum weight of an OITDIDF on G. In this paper, we establish various bounds on oi tdI (G), and we determine this parameter for some special classes of graphs.