In 2011, Benjamini, Kozma and Schapira introduced a “balanced excited random walk” in the 4-dimensional lattice. In 2016, a similar model was studied by Peres, Schapira and Sousi in the 3-dimensional lattice. Here we generalize their constructions in the d-dimensional lattice, in the following way: if the walk visits a site for the first time, it makes a simple random walk step in the first d_1 dimensions, whereas if the site has been already visited, it makes a simple random walk step in the last d_2 coordinates. Both BKS and PSS proved transience in the non-overlapping case d=d_1+d_2, with d_1=d_2=2 (BKS) and d_1=1, d_2=3 (PSS). In this talk some result for the overlapping case (d_1+d_2>d) will be presented, in particular for d=4, d_1=2 and d_2=3. (Joint work with D. Camarena and A. Ramirez).