  We present a numerical study for the threshold percolation probability,
$p_c$, in the bond percolation model with multiple ranges, in the square
lattice. A recent Theorem demonstrated by de Lima {\it et al.} [B. N. B. de
Lima, R. P. Sanchis, R. W. C. Silva, STOCHASTIC PROC APPL {\bf 121}, 2043-2048
(2011)] states that the limit value of $p_c$ when the long ranges go to
infinity converges to the bond percolation threshold in the hypercubic lattice,
$\mathbb{Z}^d$, for some appropriate dimension $d$. We present the first
numerical estimations for the percolation threshold considering two-range and
three-range versions of the model. Applying a finite size analysis to the
simulation data, we sketch the dependence of $p_c$ in function of the range of
the largest bond. We shown that, for the two-range model, the percolation
threshold is a non decreasing function, as conjectured in the cited work, and
converges to the predicted value. However, the results to the three-range case
exhibit a surprising non-monotonic behavior for specific combinations of the
long range lengths, and the convergence to the predicted value is less evident,
raising new questionings on this fascinating problem.
