  In this paper, the holographic superconductor model with two s-wave orders
from 4+1 dimensional Einstein-Gauss-Bonnet gravity is explored in the probe
limit. At different values of the Gauss-Bonnet coefficient $\alpha$, we study
the influence of tuning the mass and charge parameters of the bulk scalar field
on the free energy curve of condensed solution with signal s-wave order, and
compare the difference of tuning the two different parameters while the changes
of the critical temperature are the same. Based on the above results, it is
indicated that the two free energy curves of different s-wave orders can have
one or two intersection points, where two typical phase transition behaviors of
the s+s coexistent phase, including the reentrant phase transition near the
Chern-Simons limit $\alpha=0.25$, can be found. We also give an explanation to
the nontrivial behavior of the $T_c-\alpha$ curves near the Chern-Simons limit,
which might be heuristic to understand the origin of the reentrant behavior
near the Chern-Simons limit.
