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Let $(1\to N_n\to G_n\to Q_n\to 1)_{n\in\mathbb{N}}$ be a sequence ofextensions 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 $(G_n)_{n\in\mathbb{N}}$ issaid 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 showthat the coarse Novikov conjecture holds for spaces with an FCE-by-FCEstructure.

Higher index theory for spaces with an FCE-by-FCE structure