  We discuss how the properties of a single-channel Kondo lattice model are
modified by additional screening channels. Contrary to current wisdom,
additional screening channels appear to constitute a relevant perturbation
which destabilizes the Fermi liquid. When a heavy Fermi surface develops, it
generates zero modes for Kondo singlets to fluctuate between screening channels
of different symmetry, producing a divergent composite pair susceptibility.
Additional screening channels couple to these divergent fluctuations, promoting
an instability into a state with long-range composite order.
