  In this article, we will prove the Generalized Nonvanishing Conjecture holds
for threefolds with either $\kappa>0$ or $q>0$. As a result, we can prove the
Iitaka conjecture $C_{n,m}$ holds for $n=7$ if the source space has
non-negative Kodaira dimension, if the general fibre has positive Kodaira
dimension, or if the base space is not threefold with $\kappa=q=0$. In
particular, $C^-_{n,m}$ holds if $n\leq 7$.
