[en] 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 τ_J, j = 1 1,..., N which are all antiferromagnetically coupled to a periodic array of modul S = 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. (author). 33 refs, 1 fig