I have both Honeysuckle 'Major Wheeler' and a variety of clematis. I don't think I would put them on the same trellis since the honeysuckle is more woody and the stems twine around the support, while the clematis clings with its leaf petioles and has softer stems. I'd be worried that the woodier honeysuckle would crush the stems of the clematis. However, since I haven't tried it, I don't know that it would be a problem. They would most probably have different pruning needs as well. I'd get a second clematis that is the same pruning type and about the same size for the clematis trellis.

My MW is only in its second season, but I've seen an older one and it's quite attractive, quite thick and full with lots of blooms and foliage that I find attractive, so I've put mine by itself on an iron tuteur.