Composite fermions have played a seminal role in advancing our
understanding of the quantum Hall effect, particularly the formation of
a compressible composite Fermi liquid (CFL) at filling factor nu = 1/2.
Motivated by experiments on systems ranging from quantum Hall bilayers
to 3D bismuth, I will discuss a new kind of multi-layer CFL, wherein
interlayer Coulomb repulsion generates `metallic' behavior of composite
fermions between layers. Such `interlayer coherent CFLs' raise the
intriguing possibility that composite fermions may emerge in higher
dimensions. As a concrete example, I will propose that quantum Hall
bilayers with nu = 1/2 per layer at intermediate layer separation may
host an interlayer coherent CFL, driven by exciton
condensation of composite fermions. I will discuss the rather remarkable properties of this state, and describe a new sequence of incompressible quantum Hall states that emerge from it at nearby filling factors. Future experimental and theoretical work will also be discussed, in particular a generalization of this phase to three dimensions.