  We study the splitting of the Goodwillie towers of functors in various
settings. In particular, we produce splitting criteria for functors $F: \A \to
M_A$ from a pointed category with coproducts to $A$-modules in terms of
differentials of $F$. Here $A$ is a commutative $S$-algebra. We specialize to
the case when $\A$ is the category of $\a$-algebras for an operad $\a$ and $F$
is the forgetful functor, and derive milder splitting conditions in terms of
the derivative of $F$. In addition, we describe how triples induce operads, and
prove that, roughly speaking, a triple $T$ is naturally equivalent to the
product of its Goodwillie layers if and only if it is an algebra over its
induced operad.
