  A multi--channel generalization of Doniach's Kondo necklace model is
formulated, and its phase diagram studied in the mean--field approximation. Our
intention is to introduce the possible simplest model which displays some of
the features expected from the overscreened Kondo lattice. The $N$ conduction
electron channels are represented by $N$ sets of pseudospins $\vt_{j}$, $j=1,
... , N$, which are all antiferromagnetically coupled to a periodic array of
$|\vs|=1/2$ spins. Exploiting permutation symmetry in the channel index $j$
allows us to write down the self--consistency equation for general $N$. For
$N>2$, we find that the critical temperature is rising with increasing Kondo
interaction; we interpret this effect by pointing out that the Kondo coupling
creates the composite pseudospin objects which undergo an ordering transition.
The relevance of our findings to the underlying fermionic multi--channel
problem is discussed.
