  Cosmological scaling solutions, which give rise to a scalar-field density
proportional to a background fluid density during radiation and matter eras,
are attractive to alleviate the energy scale problem of dark energy. In the
presence of multiple scalar fields the scaling solution can exit to the epoch
of cosmic acceleration through the so-called assisted inflation mechanism. We
study cosmological dynamics of a multi-field system in details with a general
Lagrangian density p=sum_{i=1}^n X_i g(X_i e^{lambda_i phi_i}), where
X_i=-(nabla phi_i)^2/2 is the kinetic energy of the i-th field phi_i, lambda_i
is a constant, and g is an arbitrary function in terms of Y_i=X_i e^{lambda_i
phi_i}. This covers most of the scalar-field models of dark energy proposed in
literature that possess scaling solutions. Using the bound coming from
Big-Bang-Nucleosynthesis and the condition under which the each field cannot
drive inflation as a single component of the universe, we find the following
features: (i) a transient or eternal cosmic acceleration can be realized after
the scaling matter era, (ii) a "thawing" property of assisting scalar fields is
crucial to determine the evolution of the field equation of state w_{phi}, and
(iii) the field equation of state today can be consistent with the
observational bound w_{phi}<-0.8 in the presence of multiple scalar fields.
