Canaries are themselves a variety of finch. Finches tend to be sociable birds. Given enough room, canaries mix well with other finches. Best combinations include singer finches and smaller finches such as zebra, Australian, Bengalese and waxbills.
Male canaries can be territorial. Select mostly females for group and combined housing. Competition with larger or more temperamental finches can be detrimental to canaries. High-calorie diets required by some larger finches may fatten canaries. Pick the smaller varieties of finch to combine with canaries and you can avoid problems.
Combining small finches and canaries works well because, as related species, their dietary needs are similar. Zebra and other small finches survive well on canary seed supplemented with greens and millet. Supplementing seed with vegetables and sprouting seeds is standard for canary care also. Both require ground shell, cuttle fish or a mineral block. Both benefit from occasional meal worms or hard-boiled egg. When breeding, a combined "canary/finch nestling food" suits both.
Living naturally in flocks, both canaries and small finches appreciate aviary living in the company of others. Sharing similar housing needs, they appreciate flying room. Canaries and small finches both enjoy a birdbath.