multiple urls for seo rankings

The risk with multiple 301s is that Google may see that as unnatural. The risk is less if the domains are relevant and 301s are gradual. Nevertheless, each of those URLs may have some backlinks or in general may have some SEO standings. When you 301 them you basically collect all of their SEO standings in one place. It seems that all of the SEO weight of the first domain doesn't transfer to the second one but a good portion of that will transfer, so basically the main domain now has different SEO standings combined coming from different domains.
Think about it this way: You may have a business that people refer to with different names and then search for it with different names. You want to have just one website for them. So, in theory you can make as many 301s as you want to make that happen. If Google sees that as fishy, then it is another story...

O.K.

This is how it works:

- The primary domain had an initial PR assigned to it (if there was content on it) based on the content it used to have (number of pages and internal linking structure). Also it had some SEO value for different keywords built over-time. It had to do with EMD (exact match domain), on-page content and backlinks (affecting both PR of the page and its rankings for different keywords based on anchors and other link attributes). So in general it had some standings or weight or whatever you may call it for different keywords. If domain didn't have any content beforehand or any backlinks then it is going to be only exact match domain effect and domain age effect (although as far as I know, domain age is useful if there was some content on that domain. Essentially it is the age that domain was used for something, calculated from the first time search engine indexed any page on the domain).
So as summary, if your domain didn't have any pages on it, then it is going to be EMD and age effect...
Now, let's say your domain had a website on it. Some of the PR will flow to your secondary domain. Also if the website had any rankings for any keywords, some of that will transfer. Specially if it had anchored backlinks, some of the SEO effect of those backlinks will transfer to the secondary website as if they are backlinks to the secondary domain just with slightly lower effect...

Those are domains, not URLs. Are they all his domains, or yours?

If they were parked domains, there will not be any benefit to your client whatsoever. The only benefit would be from type-in traffic from people who are specifically looking for one of the redirected domains. That is not likely to happen due to the hyphenated domains.

If they were live sites that already had a lot of links pointing to them, then your client might receive a portion of the link juice that was formerly flowing to each domain. If the domains were never developed, there isn't any link juice to pass.

301 redirects do not work that the same with Google as they did a few years ago. At one time, PageRank and all link juice was passed to the new domain. Today that is discounted.

The primary risk to the redirected domains is if the primary site site gets penalized. That could affect the redirected domains, as well.

If all of the domains are his, and the redirects are proper 301 redirects, there should not be any negative effects, but there won't likely be any benefits, either.

I own and SEO company and I see no benefit in using the 301 redirects in that manner.

I think if done cleverly in a limited way, it's still a good practice.