The short answer to whether Magento can do this is yes, with Shopping Cart Price Rules. There are probably other ways of doing it, like using different Product Types and Tier Pricing or by using Catalog Price Rules, but the simplest way would probably be to do the following:
Go to Magento
Admin->Promotions->Shopping Cart Price Rules-> and click
Add New Rule
Add the required information under
Actions->Apply the rule only to cart items matching...., click the plus sign to add a condition and in the first dropdown, select
Quantity in cart, in the second dropdown, select
equals or greater than and in the last text-box, enter 3.
Discount Amount to
16.666667 and click
The result will be that any products will go from $6/each to $5/each whenever the cart has 3 or more items in it.
The answer to whether it can be added to your existing site is a little more complicated, but I would say no. Mostly because going through the trouble of creating a Magento instance just to provide that functionality, then customizing both your site and the Magento instance to work with each other is probably more trouble than it is worth. While you could use them separately, I would recommend moving the entire site to Magento, and I think the result would be a far more robust site that makes both you and your customers much happier.