  Let $(1\to N_n\to G_n\to Q_n\to 1)_{n\in\mathbb{N}}$ be a sequence of
extensions of finite groups. Assume that the coarse disjoint unions of
$(N_n)_{n \in \mathbb{N}}$, $(G_n)_{n \in \mathbb{N}}$ and $(Q_n)_{n \in
\mathbb{N}}$ have bounded geometry. The sequence $(G_n)_{n\in\mathbb{N}}$ is
said to have an \emph{FCE-by-FCE structure}, if the sequence
$(N_n)_{n\in\mathbb{N}}$ and the sequence $(Q_n)_{n\in\mathbb{N}}$ admit
\emph{a fibred coarse embedding} into Hilbert space. In this paper, we show
that the coarse Novikov conjecture holds for spaces with an FCE-by-FCE
structure.
