Yes, but why? Technically speaking, you can point as many domain names as you want to your site. You just need to let us know so that we can "receive" them on our server and set them up as "aliases" to your particular account. We charge a very small monthly fee to cover our costs. See our fees chart for details. This is a good idea if you own the .com, .net, .org, etc. versions of a single name.
However, just because it's possible to have multiple domain names pointing to the same site doesn't mean it's always a good idea. In fact we usually discourage having multiple domain names (if they are different names) because it confuses your branding and your customers.
We here at Gutensite believe strongly in the power of branding – creating one brand that people can always remember, such as Google, Flickr, and of course Gutensite. Or even just your own name as a brand. Along with that goes the principle of having one domain name that matches your brand and is easily memorable.
So, for Gutensite, when our clients want web design, they go to gutensite.com. When they want a new logo or some print work, they also go to gutensite.com. And on and on. We don't have generic urls for gutensiteprint.com or yourbestprintdesigner.com, etc. Doing so doesn't build a brand, and it prohibits you from creating a solid, reliable reputation. In fact, the opposite can happen with multiple domains – people won't remember if your site is luxurypeninsulaproperties.com, peninsulaluxuryproperties.com, or peninsulaluxury.com. They'll guess and end up at someone else's site. So having multiple domain names to the same site splits your energy and focus and keeps you from developing a single identity. But if you have one domain name like gutensite.com, that is what you brand and that is what people will remember. And when they see your advertising, they'll type in whatever you have listed there.
On a side note, there is a place for owning multiple domains that could possibly be mistyped. For example, we own gutensite.com and gutensites.com, in case someone thinks there is an "s" on the end. This is a good way to protect your brand.
However, if you still think you may need multiple domains, you need to have us set them up as a 301 redirect, so that the secondary domains redirect to your primary domain (i.e. when a domain alias is entered into the address bar, it takes you to your website and the domain alias you enetered is replaced with your main domain name in the address bar). This reinforces your brand, and also makes sure you aren't punished by search engines for Spamming (e.g. faking duplicate content on multiple "websites", i.e. domains).
So in our opinion, we believe in avoiding multiple domain names and rather choosing and promoting your brand name with one memorable domain name.