This is a topic we run into quite often actually. There is a misconception that buying a bunch of domains and pointing them to your site will some how help the ranking or overall traffic of your website. This is simply untrue.
Google and other search engines try to make the best site show up for the search terms that are entered. They have cultivated algorithms over the years that aim to eliminate anyone using money to prop up their site. Propping up ones site in the past using money included buying inbound links from all over the web and loading up on domain names. It has been a long time since these practices were of any value.
That does not mean that pointing another domain to your site is not beneficial. If the old domain has been attached to an actual working website for a long enough period of time, a person can actually get some “link juice” from the domain when they forward it to their site. This is because Google realizes that people may have multiple sites with similar subject matter and instead of shutting one down they can redirect the old followers to the new or permanent website.
The link juice created from the re-pointing of the domain will create a temporary stimulation to your site in Google. The other value it creates is when anyone who had previously bookmarked your site decides to visit it again, they are redirected to your new site.
After a short time, the search bots figure out that the redirect is permanent (301 redirect) and the search results balance out and any link juice gained form this switch will dissipate. One thing you definitely do not want to do is switch the link forwarding back and forth. This confuses to spiders at the very least and at the very worst can look deceptive to the Google algorithms. You can be brown-listed. And nobody wants that.