When I started working with the recommendations API I thought the same but I don't think that this would give very good results. As far as I can tell the recommendations API doesn't combine your seeds to come up with tracks that best meet a mixture of the seeds. If you have multiple seeds it just returns some recommendations relevant to each one.
- if you have 1 seed, you get 20 recommendations based on that seed
- if you have 2 seeds, you get about 10 recommendations based on each seed
For example, if I have 2 genre seeds: rock and soundtracks, I don't get rock music soundtracks. I get 10 recommendations of rock and 10 of (mostly orchestral) soundtracks. I'd love to think it's cleverer than that but, based on this example, I doubt it.
If you had more than 5 seeds you'd start getting just one or two recommendations for some of the seeds. You'd probably then be better off just requesting recommendations for each of the seeds separately.